http://www.coastalwiki.org/w/api.php?action=feedcontributions&user=Dronkers+J&feedformat=atomCoastal Wiki - User contributions [en]2020-01-18T00:49:09ZUser contributionsMediaWiki 1.31.3http://www.coastalwiki.org/w/index.php?title=Swash_zone_dynamics&diff=76340Swash zone dynamics2020-01-17T11:44:52Z<p>Dronkers J: </p>
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==Introduction==<br />
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[[Image: BaldockFig1.jpg|thumb|440px|left|Figure 1. Definition sketch for the nearshore littoral zone (swash zone width exaggerated). After <ref> Elfrink, B. and T. Baldock (2002). Hydrodynamics and sediment transport in the swash zone: a review and perspectives. Coastal Engineering 45: 149-167</ref>.]]<br />
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The swash zone forms the land-ocean boundary at the landward edge of the surf zone, where waves runup the beach face (figures 1, 2). It is perhaps the region of the ocean most actively used by recreational beach users and, being very visible, is the region of the littoral zone most associated with beach erosion and the impacts of climate change. The landward edge of the swash zone is highly variable in terms of geomorphology, and may terminate in dunes, cliffs, marshes, ephemeral estuaries and a wide variety of sand, gravel, rock or coral barriers. This influences the exchange of sediment between the land and ocean, which ultimately forms the coastline.<br />
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In terms of coastal processes and coastal protection, a large part of the littoral sediment transport occurs in the swash zone, both cross-shore and longshore, which influences beach morphology, and beach erosion and beach recovery during and after storms. Wave runup is an important factor in the design of coastal protection and also generates hazards for beach users, and is the dominant process leading to the erosion of coastal dunes. Swash hydrodynamics also influence the ecology of the intertidal zone and groundwater levels in sub-aerial littoral beaches and low lying islands, which is often critical for freshwater water supply on islands and atolls <ref>Nielsen P., 1999. Groundwater dynamics and salinity in coastal barriers. J. Coastal Res., 15: 732-740. </ref>. <br />
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==Characteristics of the swash zone==<br />
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[[File:BaldockFig2a.jpg|thumb|445px|left|Figure 2a. Seven Mile Beach, NSW, Australia, a dissipative beach. Photo shows conditions after a swash rundown, with only small bores reaching the swash zone. Photo: Dr Hannah Power, University of Newcastle, NSW, Australia.]]<br />
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[[File:BaldockFig2b.jpg|thumb|445px|left|Figure 2b. Avoca Beach, NSW, Australia, a reflective beach. Photo shows the inner surf zone and a bore reaching the swash zone in the background and a swash uprush reaching the top of a beach berm in the foreground.]]<br />
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The hydrodynamic processes in the swash zone are characterised by very different types of fluid flow compared to the open ocean and surf zone, as illustrated in figure 2, where the strongly orbital motion of waves is transformed into flow along the bed (velocity <math>V</math>), usually in thin shallow sheets (thickness <math>d</math>). In terms of fluid mechanics, the key difference is the occurrence of supercritical flow in the swash zone, where the Froude number,<math>V/ \sqrt{gd}</math>, is greater than 1, which has important implications for the nature of the flow. Other important distinctions are that friction becomes more important in controlling aspects of the shallow flow in the swash zone than in the surf zone, and that turbulence and sediment transport in the swash zone is generated locally in the swash zone and advected into the swash zone from the surf zone. A key feature of both the hydrodynamics and sediment dynamics in the swash zone is intermittency, where the extent and degree of inundation of the swash zone varies over different timescales, from orders of seconds and tidal periods to years and decades. This is a challenge for coastal scientists, both in terms of measurement and modelling of the physical processes. For the purposes of this summary, the swash zone will be considered as the region of the beach face exposed to the atmosphere over wind, swell and infragravity wave durations, i.e., seconds to a few minutes.<br />
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The characteristics of the swash zone hydrodynamics and sediment transport are governed by the inner surf zone and the underlying beach, with feedback of course between the morphology and hydrodynamic processes. The beach slope is a controlling parameter <ref>Guza, R. T., Thornton, E. B. and Holman, R. A., 1984. Swash on steep and shallow beaches. Proc. 19th Int. Conf. Coastal Eng., ASCE, 708-723. </ref>. On dissipative beaches, with wide surf zones, most of the wind wave and swell energy is dissipated seaward of the swash zone. Therefore, swash processes are dominated by those due to long, or [[Infragravity waves|infragravity waves]], which are frequently non-breaking standing waves (figure 2a). On intermediate and reflective beaches, short wave energy reaches the beach face in the form of bores or shore-breaks, which collapse at the beach, initiating a runup motion characterised by a thin sheet of water with a rapidly propagating wave tip which is analogous to a [[Dam break flow|dam-break flow]] over a dry bed (figure 2b). This sheet of water is slowed by gravity and friction until the flow reverses and forms another shallow flow seaward, the backwash. On coarse grained sand and [[Gravel Beaches|gravel beaches]] a significant volume of the uprush and some of the backwash may percolate into the beach, reducing the volume of water in the surface backwash flow. These two distinct types of swash zone make modelling hydrodynamic processes difficult, since parametric models rely on similarity of processes, and therefore phase resolving models of the whole surf zone, or at least the inner surf zone, are required if the details of the hydrodynamics are required. Fortunately some processes are modelled very well by parametric models, perhaps more accurately than phase-resolving models, particularly wave runup.<br />
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==Wave runup and overtopping==<br />
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[[Image: BaldockFig3NEW2.jpg|thumb|500px|left|Figure 3. Typical pattern of bore-driven swash oscillations (vertical component). Data show shoreline elevation versus time at Avoca Beach, NSW. Red and green squares indicate maxima and minima of individual swash events. Data courtesy of Dr Michael Hughes, NSW Office of Environment and Heritage.]]<br />
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Wave runup is perhaps the most important aspect of swash zone flows. While the motion of the water volume as a whole may be considered as runup, conventionally wave runup refers to the landward limit of the swash motion on the beach face, usually defined vertically above the ocean level. The runup and rundown of the shoreline is referred to as the swash excursion or oscillation. A typical plot of the shoreline motion is shown in figure 3.<br />
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Remarkably, the maximum runup is still most reliably described by a simple empirical parametric formula, which is perhaps one of the oldest regularly in use, proposed by Hunt (1959). Despite numerous variations, the underlying scaling still holds over a very large range of wave conditions, both in the laboratory and field.<br />
The scaling for runup proposed by Hunt <ref>Hunt, I.A., 1959. Design of sea-walls and breakwaters. Transactions of the American Society of Civil Engineers, 126: 542-570. </ref> is:<br />
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<math>R_{max}=\xi H_0 = \tan \beta \sqrt{H_0 L_0} , \qquad (1)</math><br />
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where <math>\xi</math> is the surf similarity parameter, or Iribarren number (<math>\xi =\tan\beta / \sqrt{H_0/L_0})</math> and <math>H_0, L_0</math> and <math>\beta</math> are offshore wave height, wave length and the swash zone beach face slope, respectively. This is strictly only applicable for monochromatic waves and the maximum runup. However, the same formulation has been widely used to describe random wave runup, using appropriate [[Statistical description of wave parameters|statistical parameters to describe the wave conditions]]. This parameter is usually the runup elevation exceeded by 2% of the waves, <math>R_{2\%}</math>. The most widely used derivative of Hunt's formula is perhaps due to Stockdon et al. <ref name=S> Stockdon, H. F., Holman, R. A., Howd, P. A. & Sallenger JR, A. H. 2006. Empirical parameterization of setup, swash, and runup. Coastal Engineering, 53, 573-588.</ref>, which also allows for a contribution from infragravity waves:<br />
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<math> R_{2\%} = 1.1 \; \left( 0.5 \sqrt{H_s L_p \; (0.563 \beta^2 + 0.004)} +0.35 \; \beta \sqrt{H_s L_p} \right) , \qquad \xi_p \ge 0.3 , \qquad (2)</math><br />
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<math> R_{2\%}= 0.43 \; \beta \sqrt{H_s L_p} , \qquad \xi_p < 0.3 , \qquad (3)</math><br />
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where the term <math>0.35 \; \beta \sqrt{H_s L_p}</math> represents the setup, <math>H_s</math> is the deep water significant wave height, and <math>L_p</math> is the wavelength corresponding to the deep water peak wave period, <math>T_p</math>. Atkinson et al. <ref>Atkinson, A.L., Power, H.E., Moura, T., Hammond, T., Callaghan, D.P. and Baldock, T.E., 2017. Assessment of runup predictions by empirical models on non-truncated beaches on the south-east Australian coast. Coastal Engineering, 119: 15-31. </ref> compared a number of recent runup formulations to measurements from a range of beaches and concluded that the models generally predict runup with errors of order <math>\pm 25 \%</math>.<br />
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[[Image: BaldockFig4.jpg|thumb|500px|left|Figure 4. Swash energy spectra from (a) reflective, (b) intermediate, and (c) dissipative beach-states. The grey lines show individual spectra, the coloured lines show the average spectrum for the beach-state, the black line represents an <math>f^{-4}</math> energy roll-off and the vertical dashed line demarcates the short-wave and long-wave frequency bands. From Hughes et al. <ref>Hughes, M. G., T. Aagaard, T. E. Baldock and H. E. Power, 2014. Spectral signatures for swash on reflective, intermediate and dissipative beaches. Marine Geology 355: 88-97. </ref>, with permission.]]<br />
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Swash-swash interactions occur through the overtaking of a swash uprush by the following bore or during the collision of the backwash flow with the next uprush. The magnitude, or vertical excursion, of the swash oscillations, from rundown position to runup, is strongly influenced by interaction between wave uprush and backwash, with the period of the incident waves also controlling the period of the swash oscillations at swell and wind wave frequencies <ref>Holman, R. A. 1986. Extreme value statistics for wave runup on a natural beach. Coastal Engineering, 9: 527-544. </ref>. Hence, given a finite time for the uprush and backwash to occur, there is a finite magnitude for a swash oscillation at a given frequency on a given beach slope if the motion is solely controlled by gravity. This leads to swash saturation, where an increase in incident wave height does not increase the magnitude of the swash oscillations. This can be parameterised for individual events, or through a spectral representation.<br />
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For non-breaking monochromatic waves, this limit is given by Miché <ref>Miché, R., 1951. Le pouvoir réfléchissant des ouvrages maritimes exposés à l'action de la houle. Ann. Ponts et Chaussees, 121: 285-319. </ref>:<br />
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<math>\varepsilon_s=\Large \frac{a_s \omega^2}{g \beta^2} \normalsize = 1 , \qquad (4)</math><br />
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where <math>a_s</math> is the vertical amplitude of the shoreline motion, <math>\omega</math> is the angular wave frequency (<math>=2 \pi f</math> - where <math>f</math> is the wave frequency), <math>g</math> the gravitational acceleration and <math>\beta</math> the beach slope. This assumes a saturated surf zone and, based on the limiting amplitude for monochromatic unbroken standing waves, <math>\varepsilon \approx 1</math>. For swash initiated by breaking wave bores, Baldock and Holmes <ref name=B>Baldock T. E. and Holmes P., 1999. Simulation and prediction of swash oscillations on a steep beach. Coastal Engineering, 36: 219-242. </ref> derived a theoretical value <math>\varepsilon \approx 2.5</math>, where saturation is controlled by swash-swash interaction as opposed to surf zone saturation. Spectra of the shoreline oscillations also indicate saturation at higher frequencies, with a typical roll-off in the energy density that is proportional to <math>f^{-4}</math>, which is also evident from equation 4. Huntley et al. <ref>Huntley, D. A., R. T. Guza and A. J. Bowen, 1977. Universal form for shoreline runup spectra. Journal of Geophysical Research-Oceans and Atmospheres 82: 2577-2581. </ref> proposed a uniform spectral form for saturated swash spectra, but variations occur due to different surf zone conditions (figure 4).<br />
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[[Image: BaldockFig5.jpg|thumb|300px|right|Figure 5. Washover fan deposited on Ocracoke Island, North Carolina, during Hurricane Isabel, September 2003. Source: Adapted from Donnelly, Kraus, and Larson (2006) <ref>Donnelly, C., N. Kraus and M. Larson, 2006. State of knowledge on measurement and modeling of coastal overwash. Journal of Coastal Research 22: 965-991. </ref>. Reproduced with permission of the Coastal Education and Research Foundation, Inc.]]<br />
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When the runup exceeds the elevation of the crest of a structure, beach berm or dunes, wave overtopping or wave overwash occurs. This process is very important in building beach berms higher, in association with the spring-neap tidal cycle, but also leads to coastal flooding and inundation of the backshore region. The geomorphology of barrier islands and gravel barriers is strongly dependent on swash overtopping, and breaching of these systems by landward transport of sediment during the overtopping can lead to rapid and potentially [[Dune erosion|catastrophic failure of protective coastal barriers]] (figure 5). The response of coastlines to sea level rise is also be influenced by swash overtopping and sediment overwash, which increases recession in comparison to the classical [[Bruun rule for shoreface adaptation to sea-level rise|Bruun Rule]] <ref>Rosati, J. D., R. G. Dean and T. L. Walton, 2013. The modified Bruun Rule extended for landward transport. Marine Geology 340: 71-81. </ref>. A combination of parametric modelling and numerical techniques is required to model these scenario <ref>Roelvink, D., Reniers, A., Van Dongeren, A.P., de Vries, J.V.T., McCall, R. and Lescinski, J., 2009. Modelling storm impacts on beaches, dunes and barrier islands. Coastal engineering, 56: 1133-1152. </ref><br />
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==Swash zone hydrodynamics==<br />
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[[Image: BaldockFig6.jpg|thumb|500px|left|Figure 6. Forward (solid) and backward (dashed) characteristic curves (a), and contours of flow velocity (b), surface elevation (c) and depth (d) for swash initiated by a near uniform bore in the non-dimensional coordinates of Peregrine and Williams <ref name=P></ref>. Dotted lines in panel (a) show locus of u=c (critical flow) for uprush and backwash. From <ref name=GB></ref>, with permission.]]<br />
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Swash zone flows have several features that differ from those in the surf zone, but this is dependent on the dominant wave conditions in the inner surf zone as noted above. Many key characteristics again depend on the Iribarren number <ref> Roos, A. and Battjes, J.A., 1977. Characteristics of flow in runup of periodic waves. Proc. 15th International Conference on Coastal Engineering, ASCE, pp. 781-795</ref>. For infragravity standing long waves, the variation in flow depth and flow velocity at a point is relatively symmetrical during uprush and backwash. Short wave bores generate more asymmetrical flows, with the maximum velocity occurring at the start of inundation, with a rapid rise to the maximum depth, with an almost linear deceleration to flow reversal, and a correspondingly similar uniform acceleration in the backwash, at least until the flow becomes very shallow, when friction retards the flow significantly. A key aspect of these flows is diverging flow, which means the swash lens thins rapidly.<br />
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Runup and backwash velocities in the field reach 2-5 m/s, which are generally larger than those in the surf zone. The runup durations are typically shorter than the backwash duration, and the backwash depths are shallower than during the uprush, and therefore the velocity moments tend to be skewed offshore, which has important implications for the sediment dynamics <ref>Raubenheimer, B., R. T. Guza, S. Elgar and N. Kobayashi, 1995. Swash on a gently sloping beach. Journal of Geophysical Research-Oceans 100(C5): 8751-8760. </ref>. The asymmetry is however affected by the mass and momentum advected into the swash zone, which depends on the flow in the inner surf zone. Self-similar solutions for different boundary conditions are presented by Guard and Baldock <ref name=GB>Guard, P. A. and T. E. Baldock, 2007. The influence of seaward boundary conditions on swash zone hydrodynamics. Coastal Engineering 54: 321-331. </ref>, following the work of Peregrine and Williams <ref name=P>Peregrine, D. H. and S. M. Williams, 2001. Swash overtopping a truncated plane beach. Journal of Fluid Mechanics 440: 391-399. </ref>, figure 6. These indicate the fundamental nature of the hydrodynamics, which comprise of a near parabolic motion of the shoreline (due to gravity being the dominant process) and a saw-tooth shaped variation in velocity with time, which decreases at a near linear rate from the peak velocity, which occurs as the shoreline passes a given location. The water surface slope dips seaward for nearly the whole swash cycle, i.e. the total fluid acceleration is offshore throughout the swash cycle.<br />
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This results in a key difference between the surf zone and swash zone bed boundary conditions, namely that there is generally little phase lag between velocity and the bed shear stress in the swash zone, i.e. maxima in bed shear stress occur close to the instants of maxima in velocity. Close to the time of flow reversal, the flow near the bed does however reverse prior to the flow higher in the water column, due to the adverse pressure gradient during the uprush <ref>Kikkert, G. A., T. O'Donoghue, D. Pokrajac and N. Dodd, 2012. Experimental study of bore-driven swash hydrodynamics on impermeable rough slopes. Coastal Engineering 60: 149-166. </ref>. The boundary layer is thinnest at the seaward edge of the swash zone during uprush, and grows following the flow up the beach. The boundary layer largely vanishes at flow reversal, and again grows from the bed as the flow recedes. Accounting for such processes in sediment transport models remains to be tackled.<br />
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[[Image: BaldockFig7NEW.jpg|thumb|400px|right|Figure 7. Contours of surface elevation with two different resistance coefficients, R=0 (blue lines) and R=0.01 (red dashed lines) in the non-dimensional coordinates of Peregrine and Williams <ref name=P></ref>. From Deng et al. <ref>Deng, X., H. Liu, Z. Jiang and T. E. Baldock, 2016. Swash flow properties with bottom resistance based on the method of characteristics. Coastal Engineering 114: 25-34</ref>, with permission.]]<br />
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There are several sources of turbulence in the swash zone. In the runup, turbulence is advected from the inner surf zone, which combines with further generation of turbulence at the bed. The boundary layer is evolving, generally increasing in thickness and may become depth limited. During the backwash turbulence generation occurs mainly at the bed, with swash-swash interactions generating further turbulence as the next wave arrives. Overall, the high turbulence near the bed leads to high bed shear stresses and the potential for high concentrations of suspended sediment transport <ref>Puleo, J. A., R. A. Beach, R. A. Holman and J. S. Allen, 2000. Swash zone sediment suspension and transport and the importance of bore-generated turbulence. Journal of Geophysical Research-Oceans 105(C7): 17021-17044. </ref>.<br />
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Friction plays a large role in controlling the shoreline motion, with friction factors based on conventional fluid mechanics principles typically in the range <math>0.02<f<0.1</math>. Friction effects are strongest when the flow is shallowest, at the swash tip, reducing runup excursions, and late in the backwash, so the shoreline recedes more slowly. Simple models, comprising of a ballistic motion plus friction, describe the shoreline motion reasonably well, although details are missing <ref>Hughes M. G., 1995. Friction factors for wave uprush. J. Coastal Res., 13: 1089-1098</ref><ref name=PH>Puleo, J. A. and K. T. Holland, 2001. Estimating swash zone friction coefficients on a sandy beach. Coastal Engineering 43: 25-40</ref>. Inclusion of friction effects in the internal flow requires numerical modelling at present, or the use of integral models which can avoid the uncertainty in the treatment of friction at the shoreline <ref>Archetti, R. and M. Brocchini, 2002. An integral swash zone model with friction: an experimental and numerical investigation. Coastal Engineering 45: 89-110. </ref>. However, recent results suggest that the effects of friction on the internal flow are small compared to the effects at the swash tip. For example, figure 7 shows a method of characteristics solution for the swash flow with and without friction. The numerical results indicate that the two solutions are similar when water is present, which is interesting given the significant effect of friction on the location of the shoreline. The reason is the supercritical nature of the flow, which is a particular feature of the swash zone. This means that the large change in the shoreline position due to friction does not significantly affect the flow seaward of the shoreline until the flow becomes subcritical, which does not occur until late in the uprush. Similarly, the supercritical nature of the backwash flow means that the changes to the shoreline position further landward cannot significantly affect flow further seaward. Thus, the supercritical nature of the swash flow means that the significant changes in shoreline position do not significantly affect the flow in the interior of the swash lens.<br />
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==Sediment transport mechanics==<br />
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[[Image: BaldockFig8.jpg|thumb|400px|left|Figure 8. A turbulent bore containing entrained suspended sediment just prior to reaching the swash zone. The sediment is then advected into the swash zone during the runup. The end of a supercritical backwash flow is visible in the right of the image. The posts are 1m apart and the orange stringlines are horizontal. Source: Adapted from Hughes, Aagaard, and Baldock (2007) <ref name=H></ref>. Reproduced with permission of the Coastal Education and Research Foundation, Inc.]]<br />
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Cross-shore sediment transport in the swash zone generally occurs as a combination of bed load under sheet flow conditions, with a flat bed, plus an additional component of suspended load, generated locally and advected into the swash zone by surf zone bores. For the bed load, the Meyer-Peter and Muller <ref> Meyer-Peter, E. and Müller, R., 1948. Formulas for bed-load transport. Proc. IAHR, Stockholm </ref> formulation, or derivatives, generally perform well with calibration, i.e. determining the transport coefficient and friction factor remain problematic. In these models, the transport is typically a function of the velocity cubed (see for a more detailed discussion the article [[Sand transport]]). The relative balance between bed load, which is generated locally, and suspended load depends on the sediment grain size, and also on the quantity of sediment advected into the swash zone from the inner surf zone (figure 8). This can be considerable, and affects the distribution of suspended load across the swash zone. While the basic sediment transport equations still apply, model-data comparisons are lacking, particularly close to the bed where suspended sediment concentrations are largest.<br />
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[[Image: BaldockFig9.jpg|thumb|350px|right|Figure 9. Measured normalized suspended sediment concentration <math>c </math> indicated by colours mapped onto the normalised <math>x_* - t_*</math> plane representing the swash excursion and duration. Colour bar indicates normalised concentration from high (hot) to low (cold). Source: Adapted from Hughes, Aagaard, and Baldock (2007) <ref name=H></ref>. Reproduced with permission of the Coastal Education and Research Foundation, Inc.]]<br />
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In simple <math>u^3</math> type sediment transport models the asymmetry of the flow tends to export sediment from the swash zone. In reality, this is balanced by the suspended sediment imported and advected into the swash zone from the inner surf <ref name=H>Hughes, M. G., T. Aagaard and T. E. Baldock, 2007. Suspended sediment in the swash zone: Heuristic analysis of spatial and temporal variations in concentration. Journal of Coastal Research 23: 1345-1354. </ref>, the distribution of which is illustrated in figure 9. Measurement of suspended sediment in the backwash remains a challenge, and is difficult to separate from bed-load. The quantity of suspended load entering the swash zone affects the net deposition pattern, and hence zones of erosion or accretion, as illustrated by Pritchard and Hogg <ref>Pritchard, D. and A. J. Hogg, 2005. On the transport of suspended sediment by a swash event on a plane beach. Coastal Engineering 52: 1-23</ref>. Data is still lacking in the field to reliably quantify this process, which is complicated by sediment suspended by swash-swash interactions and the influence of turbulence in the inner surf zone, which is significant <ref>Butt, T., P. Russell, J. Puleo, J. Miles and G. Masselink, 2004. The influence of bore turbulence on sediment transport in the swash and inner surf zones. Continental Shelf Research 24(7-8): 757-771. </ref>. The infiltration and exfiltration of water into the beach during swash flows is an important contributor to groundwater processes, particularly on coarse grain beaches, and also influences sediment transport <ref>Turner, I.L. and G. Masselink, 1998. Swash infiltration-exfiltration and sediment transport. Journal of Geophysical Research, 103(C13): 30,813-30,824</ref>.<br />
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The mechanics of longshore sediment transport in the swash zone are well-understood in principle, but data and modelling is limited, despite the clear presence of a significant contribution to the total [[Littoral drift and shoreline modelling|longshore transport in the littoral zone]]. In the swash zone the flow direction during both runup and rundown has a longshore component under oblique waves (the usual case). The boundary between the surf and swash zone is also an active region of longshore transport, particularly on steep cobble or coral beaches, where sediment may also move offshore into the inner surf zone, then alongshore, and then back onshore as the wave conditions or tide change <ref>Kench, P. S., E. Beetham, C. Bosserelle, J. Kruger, S. M. L. Pohler, G. Coco and E. J. Ryan, 2017. Nearshore hydrodynamics, beach face cobble transport and morphodynamics on a Pacific atoll motu. Marine Geology 389: 17-31. </ref>. While the relative importance of longshore transport in the swash zone compared to the surf zone is greater during milder wave conditions than during storms, longshore sediment transport in the swash zone may account for up to 50% of the total longshore transport <ref>Kamphuis J. W., 1991. Alongshore sediment transport rate distribution. Coastal Sediments '91 Conference, ASCE, 170-183. </ref>. Longshore transport in the swash zone is also relatively more important on steep beaches and where small oblique waves break frequently at the shoreline, e.g., in estuary mouths and landward of lagoons behind fringing and barrier reefs.<br />
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==Morphodynamics==<br />
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The evolution of the beach face in the swash zone is controlled by the sediment fluxes across the boundaries, both longshore and cross-shore. Thus, the morphology is influenced by the presence of dunes, cliffs and hard structures at the landward extent of the beach, by conditions in the inner surf one, notably bars, rip cells, beach steps, and by lateral boundaries such as groynes, breakwaters and estuary mouths. While the general processes are again well understood, and similar to those applied for littoral transport in the surf zone, the details of [[Dune erosion|dune erosion]], barrier degradation and progradation and the short and long term balance of sediment deposition and erosion remain a challenge <ref> Masselink, G. and J. A. Puleo (2006). Swash-zone morphodynamics. Continental Shelf Research 26(5): 661-680</ref>. For example, rates of deposition and erosion vary significantly on wave-by-wave time scales, wave group time-scales, and tidal time-scales, plus seasonal and annual changes due to variations in wave and wind climate. Further, while the active swash zone is usually relatively plane (excluding dunes), feedback between morphology and hydrodynamics does lead to more complex morphology such as [[Beach Cusps]]. Varying tides also lead to the formation of beach ridges and berms at different elevations, which complicate the overall topography. Dunes act as significant sources and sinks of sediment that control swash zone morphodynamics and that of the whole beach, and are essential in developing the sediment budget for the whole beach. A further aspect is the influence of vegetation, which can provide important [[Dune stabilisation|stabilising mechanisms for dunes]]. The upper beach and swash zone is where the impacts of sea level rise will be most visible, with loss of the upper beach if the coastline cannot recede landward.<br />
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==Measurement techniques==<br />
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[[Image: BaldockFig10.jpg|thumb|500px|left|Figure 10. A LIDAR system mounted above the swash zone, together with ultrasonic distance point sensors. Photo: Dr Chris Blenkinsopp, University of Bath, UK.]]<br />
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Research on swash zone processes is both assisted and hindered by the nature of the swash. The beach face is generally accessible for deployment of instruments, particularly with the aid of large tides, it is close to the shore and associated infrastructure, and much wave energy has been dissipated in the surf zone. However, flows are very shallow and also intermittent, making measurements over the depth difficult and time-averaging complex. In terms of in-situ instruments, the shoreline motion can be measured by runup wires or point instruments such as pressure sensors or ultrasonic sensors, flow velocity with electromagnetic or acoustic instruments, and morphology changes with standard survey techniques or ultrasonic sensors. To tackle larger scales and to avoid in-situ measurements and to sample over longer time-scales, [[Argus applications|remote sensing by video]] has adopted techniques first developed for the surf zone by Aagaard and Holm <ref>Aagaard, T. and J. Holm, 1989. Digitization of wave runup using video records. Journal of Coastal Research 5: 547-551. </ref> to determine friction factors <ref name=PH></ref>, runup <ref name=S></ref> and internal kinematics <ref>Power, H. E., R. A. Holman and T. E. Baldock, 2011. Swash zone boundary conditions derived from optical remote sensing of swash zone flow patterns. Journal of Geophysical Research, Oceans 116, C06007, doi:10.1029/2010JC006724</ref>. Shore-mounted LIDAR is becoming a promising tool for high resolution and long term monitoring <ref>Blenkinsopp, C. E., M. A. Mole, I. L. Turner and W. L. Peirson, 2010. Measurements of the time-varying free-surface profile across the swash zone obtained using an industrial LIDAR. Coastal Engineering 57(11-12): 1059-1065. </ref>, figure 10. However, both these techniques suffer from loss of resolution in the thinning backwash, and do not provide flow velocity with any degree of reliability. Sediment transport measurements using sediment traps <ref>Horn, D. P. and T. Mason, 1994. Swash zone sediment transport modes. Marine Geology 120(3-4): 309-325. </ref><ref> Masselink, G. and M. Hughes (1998). Field investigation of sediment transport in the swash zone. Continental Shelf Research 18(10): 1179-1199</ref> still provide the most reliable measure of total load transport rates in the field, supplemented by sediment transport rates derived from morphological measurements through sediment continuity, which can be particularly useful during overwash events. Both techniques require predominantly cross-shore transport.<br />
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==Related articles==<br />
: [[Beach Cusps]]<br />
: [[Infragravity waves]]<br />
: [[Gravel Beaches]]<br />
: [[Shallow-water wave theory]]<br />
: [[Dam break flow]]<br />
: [[Sand transport]]<br />
: [[Rhythmic shoreline features]]<br />
: [[Bruun rule for shoreface adaptation to sea-level rise]]<br />
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==References==<br />
<references/><br />
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{{author<br />
|AuthorID=34603<br />
|AuthorFullName=Tom Baldock<br />
|AuthorName= Tom Baldock}}<br />
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[[Category:Physical coastal and marine processes]]<br />
[[Category:Beaches]]<br />
[[Category:Sediment]]<br />
[[Category:Hydrodynamics]]<br />
[[Category:Morphodynamics]]</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Sand_transport&diff=76339Sand transport2020-01-17T11:38:03Z<p>Dronkers J: </p>
<hr />
<div><br />
==General characteristics==<br />
<br />
Sand can be transported by gravity-, wind-, wave-, tide- and density-driven currents (current-related transport), by the oscillatory water motion itself (wave-related transport) as caused by the deformation of short waves under the influence of decreasing water depth (wave asymmetry) or by a combination of currents and short waves. <br />
In rivers the gravity-induced flow generally is steady or quasi-steady generating bed load and suspended load transport of particles in conditions with an alluvial river bed. A typical feature of sediment transport along an alluvial bed is the generation of bed forms from small-scale ripples (order 0.1 m) up to large-scale dunes (order 100 m). The adjustment of large-scale bed forms such as dunes and sand waves may lead to non-steady effects (hysteresis effects) as it takes time for these large-scale features to adjust to changed flow conditions (flood waves). <br />
<br />
In the lower reaches of the river (estuary or tidal river) the influence of the tidal motion may introduce non-steady effects with varying current velocities and water levels on a diurnal or semi-diurnal time scale. Furthermore, density-induced flow may be generated due to the interaction of fresh river water and saline sea water (salt wedge). In coastal waters, sediment transport processes are strongly affected by high-frequency waves introducing oscillatory motions acting on the particles. The high-frequency (short) waves generally act as sediment stirring agents; net sediment transport is due to the mean current. <br />
<br />
Field experience over a long period of time in the coastal zone has led to the notion that storm waves cause sediments to move offshore while fair-weather waves and swell return the sediments shorewards. During conditions with low non-breaking waves, onshore-directed transport processes related to wave-asymmetry and wave-induced streaming are dominant, usually resulting in accretion processes in the beach zone. During high-energy conditions with breaking waves (storm cycles), the beach and dune zone of the coast are attacked severely by the incoming waves, usually resulting in erosion processes. <br />
<br />
<br />
==Definitions== <br />
<br />
Sand transport is herein defined as the transport of particles with sizes in the range of 0.05 to 2 mm as found in the bed of rivers, estuaries and coastal waters. The two main modes of sand transport are bed-load transport and suspended load transport. <br />
<br />
Bed-load transport is defined to consist of gliding, rolling and saltating particles in close contact with the bed and is dominated by flow-induced drag forces and by gravity forces acting on the particles. The suspended load transport is the irregular motion of the particles through the water column induced by turbulence-induced drag forces on the particles. Detailed information is presented by Van Rijn <ref name=Rijn93> Van Rijn, L.C., 1993, 2012. Principles of sediment transport in rivers, estuaries and coastal seas. Aqua Publications, Amsterdam, The Netherlands (WWW.AQUAPUBLICATIONS.NL)</ref>. The definition of bed-load transport is not universally agreed upon. Sheet flow transport at high bed-shear stresses may be considered as a type of bed-load transport, but it may also be seen as suspended load transport. Some regard bed-load transport as occurring in the region where concentrations are so high that grain-grain interactions are important, and grains are not supported purely by fluid forces. <br />
<br />
Suspended load transport can be determined by depth-integration of the product of sand concentration and fluid velocity from the top of the bed-load layer to the water surface. Herein, the net (averaged over the wave period) total sediment transport in coastal waters is defined as the vectorial sum of net the bed load <math>q_b</math> and net suspended load <math>q_s</math> transport rates: <br />
<br />
<math>q_{tot}=q_b+q_s</math>.<br />
<br />
For practical reasons, suspended transport in coastal waters will be subdivided into current-related and wave-related transport components. Thus, the suspended sand transport is represented as the vectorial sum of the current-related (<math>q_{s,c}</math> in current direction) and the wave-related (<math>q_{s,w}</math> in wave direction) transport components, as follows:<br />
<br />
<math>\vec q_s=\vec q_{s,c} + \vec q_{s,w}=\int \vec{v} cdz + \int <(\vec V - \vec v)(C-c)>dz , \qquad (1) </math> <br />
<br />
in which: <br />
<br />
<math>q_{s,c}</math> = time-averaged current-related suspended sediment transport rate,<br />
<br />
<math>q_{s,w}</math> = time-averaged wave-related suspended sediment transport rate (oscillating component), <br />
<br />
<math>v</math> = time-averaged velocity, <math>V</math> = instantaneous velocity, <br />
<br />
<math>C</math> = instantaneous concentration, <math>c</math> = time-averaged concentration, <br />
<br />
<math><f></math> represents averaging over time, <math> \int f dz</math> represents the integral from the top of the bed-load layer to the water surface. <br />
<br />
The precise definition of the lower limit of integration is of essential importance for accurate determination of the suspended transport rates. Furthermore, the velocity and concentration profiles must be known. <br />
<br />
The current-related suspended transport component <math>q_{s,c}</math> is defined as the advective transport of sediment particles by the time-averaged (mean) current velocities (longshore currents, rip currents, undertow currents); this component therefore represents the transport of sediment carried by the steady flow. <br />
In the case of waves superimposed on the current both the current velocities and the sediment concentrations will be affected by the wave motion. It is known that the wave motion reduces the current velocities near the bed while, in contrast, the near-bed concentrations are strongly increased due to the stirring action of the waves. These effects are included in the current-related transport. <br />
The wave-related suspended sediment transport <math>q_{s,w}</math> is defined as the transport of sediment particles by the high-frequency and low-frequency oscillating fluid components (cross-shore orbital motion). <br />
The suspended transport vector can be combined with the bed load transport vector to obtain the total transport vector: <math>q_{tot}</math>.<br />
<br />
In this note only the current-related bed load and suspended load transport components are considered. Usually, these components are dominant in river and tidal flows and also in wave-driven longshore flows.<br />
<br />
<br />
==Sand transport in steady river flow==<br />
<br />
===Basic characteristics===<br />
<br />
The transport of bed material particles may take place either as bed-load or as bed-load plus suspended load, depending on the size of the bed material particles and the flow conditions. The suspended load may also contain some wash load (usually, clay and silt particles smaller than 0.05 mm), which is generally defined as the portion of suspended load which is governed by the upstream supply rate and not by the composition and properties of the bed material. The wash load is mainly determined by land surface erosion (rainfall, no vegetation) and not by channel bed erosion. Although in natural conditions there is no sharp division between bed-load transport and suspended load transport, it is necessary to define a layer with bed-load transport for mathematical representation. <br />
<br />
When the value of the bed-shear velocity just exceeds the critical value for initiation of motion, the particles will be rolling and sliding or both, in continuous contact with the bed. For increasing values of the bed-shear velocity, the particles will be moving along the bed by more or less regular jumps, which is called saltation. When the value of the bed-shear velocity exceeds the fall velocity of the particles, the sediment particles can be lifted to a level at which the upward turbulent forces will be comparable with or of higher order than the submerged weight of the particles and as result the particles may go in suspension.<br />
<br />
The sediment transport in a steady uniform current over an alluvial bed is assumed to be equal to the transport capacity defined as the quantity of sediment that can be carried by the flow without net erosion or deposition, given sufficient availability of bed material (no armour layer). <br />
In general, a river flood wave is a relatively slow process with a time scale of a few days. Consequently, the sediment transport process in river flow can be represented as a quasi-steady process. Therefore, the available bed-load transport formulas and suspended load transport formulas can be applied for transport rate predictions. <br />
Flume and field data show that the sand transport rate is most strongly related to the depth-averaged velocity. The power of velocity is approximately 3 - 4. <br />
<br />
The bed material in natural conditions consists of non-uniform sediment particles. The effect of the non-uniformity of the sediments will result in selective transport processes (grain sorting). Grain sorting is related to the selective movement of sediment particles in a mixture near incipient motion at low bed-shear stresses and during generalized transport at higher shear stresses. Sorting effects can only be represented by taking the full size composition of the bed material, which may vary horizontally and vertically, into account. <br />
<br />
<br />
===Initiation of motion===<br />
<br />
[[Image:VanRijnFig1.jpg|thumb|500px|right|Figure 1: Initiation of motion according to Shields<ref name=Shields> Shields, A., 1936. Anwendung der Ähnlichkeitsmechanik und der Turbulenz Forschung auf die Geschiebebewegung. Mitt. der Preuss. Versuchsamst. für Wasserbau und Schiffbau, Heft 26, Berlin, Deutschland</ref> as function of Reynolds number.]]<br />
<br />
Particle movement will occur when the instantaneous fluid force on a particle is just larger than the instantaneous resisting force related to the submerged particle weight and the friction coefficient. The degree of exposure of a grain with respect to surrounding grains (hiding of smaller particles resting or moving between the larger particles) obviously is an important parameter determining the forces at initiation of motion. Cohesive forces are important when the bed consists of appreciable amounts of clay and silt particles.<br />
The driving forces are strongly related to the local near-bed velocities. In turbulent flow conditions the velocities are fluctuating in space and time. This makes together with the randomness of both particle size, shape and position that initiation of motion is not merely a deterministic phenomenon but a stochastic process as well.<br />
The fluid forces acting on a sediment particle resting on a horizontal bed consist of skin friction forces and pressure forces. The skin friction force acts on the surface of the particles by viscous shear. The pressure force consisting of a drag and a lift force is generated by pressure differences along the surface of the particle. These forces per unit bed surface area can be reformulated in a time-averaged bed-shear stress.<br />
<br />
Initiation of motion in steady flow is defined to occur when the dimensionless bed-shear stress <math>\theta</math> is larger than a threshold value <math>\theta_{cr}</math>. Thus, <math>\theta > \theta_{cr}</math> , with: <br />
<br />
<math>\theta = \tau_b / [(\rho_s-\rho_w) g d_{50}]</math> = Shields parameter, <math>d_{50}</math> = medium grain size, <math>\tau_b </math> = bed-shear stress, <br />
<br />
<math>\rho_s</math> = sediment density, <math>\rho_w</math> = fluid density, <math>d_{50} </math> = median sediment diameter.<br />
<br />
[[Image:VanRijnFig2.jpg|thumb|500px|right|Figure 2: Initiation of motion and suspension as function of dimensionless sediment size <math>D_*</math>.]]<br />
<br />
The <math>\theta_{cr}</math>- factor depends on the hydraulic conditions near the bed, the particle shape and the particle position relative to the other particles. The hydraulic conditions near the bed can be expressed by the Reynolds number <br />
<br />
<math>Re_* = u_* d/\nu</math>, where <br />
<br />
<math>u_*</math> = bed shear velocity , <math>d</math> = grain diameter, <math>\nu </math> = kinematic viscosity <math>(\sim 10^{-6}).</math> Thus: <math>\theta_{cr}= F(Re_*)</math> . <br />
<br />
Many experiments have been performed to determine the <math>\theta_{cr}</math>- values as a function of <math>Re_*</math>. The experimental results of Shields <ref name=Shields> </ref> related to a flat bed surface are most widely used to represent the critical conditions for initiation of motion (see Figure 1). The curve represents a critical stage at which only a minor part (say 1% to 10%) of the bed surface is moving.<br />
<br />
Initiation of motion in combined steady and oscillatory flow (wave motion) can also be expressed in terms of the Shields parameter or as function of a dimensionless particle size <math>D_*</math><ref name=Rijn93></ref>.<br />
<br />
The <math>D_*</math>-parameter is defined as: <br />
<br />
<math>D_*= [u_*d/(\nu \sqrt{\theta}]^{2/3} = d [(s-1) g / \nu^2]^{1/3}</math> , with:<br />
<br />
<math>g</math> = acceleration of gravity, <math>s = \rho_s/\rho_w</math> = relative density.<br />
<br />
A simple expression for initiation of motion (movement of particles along the bed) is given by Soulsby<ref name=Soul>Soulsby, R., 1997. Dynamics of marine sands. Thomas Telford, UK</ref>:<br />
<br />
<math> \theta_{cr,motion} = 0.3/(1+1.2 D_*) + 0.055 [1 - \exp(-0.02 D_*)] . \qquad (2) </math> . <br />
<br />
A simple expression for initiation of suspension (particles moving in suspension) is given by:<br />
<br />
<math> \theta_{cr,susp} = 0.3/(1+D_*) + 0.1 [1 - \exp(-0.05 D_*)] . \qquad (3) </math> . <br />
<br />
Equations (2) and (3) are shown in Figure 2.<br />
<br />
Both equations can be used to compute the critical depth-averaged velocity for initiation of motion and suspension, as follows:<br />
<br />
<math>U_{cr,motion} = 5.75 [\log(2h/d_{50})] [\theta_{cr,motion} (s-1) g d_{50}]^{0.5} , \qquad (4) </math> <br />
<br />
<math>U_{cr,susp} = 5.75 [\log(2h/d_{50})] [\theta_{cr, susp } (s-1) g d_{50}]^{0.5} , \qquad (5) </math> <br />
<br />
with: <math>U</math> = depth-averaged velocity, <math>C = 5.75 \sqrt{g} \log(4h/d_{90})</math> = Chézy coefficient, <br />
<br />
<math>h</math> = water depth, <math>d_{90} \approx 2d_{50}</math> = 90% particle size. <br />
<br />
Simple approximation formulas (10% accurate) are:<br />
<br />
<math>U_{cr,motion} = 0.19 (d_{50})^{0.1} \log(2h/d_{50})</math> for <math>0.0001<d_{50} < 0.0005 \; m ; </math><br />
<br />
<math>U_{cr,motion} = 8.5 (d_{50})^{0.6} \log(2h/d_{50})</math> for <math>0.0005<d_{50} < 0.002 \; m ; \qquad (6) </math> <br />
<br />
<math>U_{cr,susp} = 2.8 (h/d_{50})^{0.1} [(s-1) g d_{50}]^{0.5}</math> for <math>0.0001<d_{50} < 0.002 \; m . \qquad (7) </math> <br />
<br />
Figure 3 shows the critical depth-averaged velocities at initiation of motion and suspension for sediment with <math>d_{50}</math> between 0.1 and 2 mm based on Equations (4) and (5).<br />
<br />
[[Image:VanRijnFig3.jpg|thumb|600px|center|Figure 3: Depth-averaged velocity at initiation of motion and suspension.]]<br />
<br />
<br />
===Bed load transport===<br />
<br />
The transport of particles by rolling, sliding and saltating is known as bed-load transport. For example, Bagnold<ref> Bagnold, R.A., 1956. The Flow of Cohesionless Grains in Fluids. Proc. Royal Soc. Philos.Trans., London, Vol. 249.</ref> defines the bed-load transport as that in which the successive contacts of the particles with the bed are strictly limited by the effect of gravity, while the suspended-load transport is defined as that in which the excess weight of the particles is supported by random successions of upward impulses imported by turbulent eddies. Einstein<ref name=Einstein> Einstein, H.A., 1950. The Bed-Load Function for Sediment Transportation in Open Channel Flow. Technical Bulletin No. 1026, U.S. Dep. of Agriculture, Washington, D.C.</ref>, however, has a somewhat different approach. He defines the bed-load transport as the transport of sediment particles in a thin layer of 2 particle diameters thick just above the bed by sliding, rolling and sometimes by making jumps with a longitudinal distance of a few particle diameters. The bed layer is considered as a layer in which the mixing due to turbulence is so small that it cannot influence the sediment particles, and therefore suspension of particles is impossible in the bed-load layer. Further, Einstein assumes that the average distance travelled by any bed-load particle (as a series of successive movements) is a constant distance of 100 particle diameters, independent of the flow condition, the transport rate and the bed composition. In the view of Einstein, the saltating particles belong to the suspension mode of transport, because the jump lengths of saltating particles are considerably larger than a few grain diameters.<br />
<br />
The first reliable empirical bed load transport formula was presented by Meyer-Peter and Mueller<ref> Meyer-Peter, E. and Mueller, R., 1948. Formulas for Bed-Load Transport. Sec. Int. IAHR congress, Stockholm, Sweden.</ref>. They performed flume experiments with uniform particles and with particle mixtures. Based on data analysis, the following simple formula for bedload transport <math>q_b</math> was obtained, which is frequently used:<br />
<br />
<math>\Large\frac{q_b}{\sqrt{g (s-1) d_{50}^3}}\normalsize = m \, (\theta - \theta_{cr,motion})^n , </math><br />
<br />
where <math>s=\rho_s / \rho_w</math> and for <math>\theta_{cr,motion}</math> Eq. (2) can be used. For the dimensionless parameters <math>m</math> and <math>n</math> they advised the values <math>m=8</math> and <math>n=1.5</math>. In other studies a best fit to experimental data was found with values in the range <math>4<m<12</math> and <math>1.4<n<1.65</math>. <br />
<br />
Einstein<ref name=Einstein></ref> introduced statistical methods to represent the turbulent behaviour of the flow. Einstein gave a detailed but complicated statistical description of the particle motion in which the exchange probability of a particle is related to the hydrodynamic lift force and particle weight. Einstein proposed <math>d_{35}</math> as the effective diameter for particle mixtures and <math>d_{65}</math> as the effective diameter for grain roughness.<br />
<br />
Bagnold<ref> Bagnold, R.A., 1966. An Approach to the Sediment Transport Problem from General Physics. Geological Survey Prof. Paper 422-I, Washington.</ref> introduced an energy concept and related the sediment transport rate to the work done by the fluid.<br />
<br />
Engelund and Hansen<ref> Engelund, F. and Hansen, E., 1967. A Monograph on Sediment Transport in Alluvial Streams. Teknisk Forlag, Copenhagen, Denmark.</ref> presented a simple and reliable formula for the total load transport <math>q_{total}</math> in rivers:<br />
<br />
<math>\Large\frac{q_{total}}{\sqrt{g (s-1) d_{50}^3}}\normalsize = m \, \theta^{\, n} , </math><br />
<br />
with recommended values <math>n=2.5</math> and <math>m=0.04 / c_D</math>. The drag coefficient , which is defined as <math>c_D=\tau_b/(\rho u^2)</math>, is related to the Chezy coefficient <math>C \approx 5.75 \sqrt{g} \, \log_{10}(4 h / d_{90})</math> by <math>c_D=g/C^2</math>. This formula includes suspended load transport, but ignores phase lag effects of sediment suspension and settling. These phase lag effects can be important in non-steady flows. Therefore, in non-steady flows the Engelund-Hansen formula is not as accurate as total load formulas in which suspended load is computed with the formulas presented in the next sections.<br />
<br />
<br />
Van Rijn<ref> Van Rijn, L.C., 1984a. Sediment Transport, Part I: Bed Load Transport. Journal of Hydraulic Engineering, ASCE, Vol. 110, No. 10</ref> solved the equations of motions of an individual bed-load particle and computed the saltation characteristics and the particle velocity as a function of the flow conditions and the particle diameter for plane bed conditions. The results of sensitivity computations show that the bed load transport is only weakly affected by particle diameter. A 25%-variation of the particle diameter (<math>d_{50} = 0.8 \pm 0.2 \; mm</math>) results in a 10%-variation of the transport rate.<br />
<br />
Bed load transport <math>q_b</math> can be determined from the measured bed form dimensions and the measured bed form migration velocity using echo sounding results. The bed load transport is by definition: mass <math>m_s</math> per unit area of bed times migration velocity <math>c</math>: <math> q_b= c m_s </math>. <br />
The mass <math>M_s</math> of a triangular bed form with length <math>L</math>, height <math>\Delta H</math>, sediment density <math>\rho_s (\approx 2650 kg/m^3) </math> and porosity <math>p (\approx 0.4)</math> is <math>M_s = 0.5 \rho_s (1-p) L \Delta H </math>.<br />
The mass per unit area is the mass <math>M_s</math> divided by the length <math>L</math> giving <math>m_s = 0.5 \rho_s (1-p) \Delta H</math>. Bed load transport is thus given by: <br />
<br />
<math>q_b = 0.5 \rho_s (1-p)c \Delta H </math>.<br />
<br />
As bed forms are not fully triangular, a more general expression is: <br />
<br />
<math>q_b= \alpha \rho_s (1-p) c \Delta H </math>, with <math>\alpha = 0.5 - 0.7</math>.<br />
<br />
<br />
===Suspended load transport===<br />
<br />
[[Image:VanRijnFig5.jpg|thumb|500px|right|Figure 4: Definition sketch of suspended sediment transport.]]<br />
<br />
When the value of the bed-shear velocity exceeds the particle fall velocity, the particles can be lifted to a level at which the upward turbulent forces will be comparable to or higher than the submerged particle weight resulting in random particle trajectories due to turbulent velocity fluctuations. The particle velocity in longitudinal direction is almost equal to the fluid velocity. Usually, the behaviour of the suspended sediment particles is described in terms of the sediment concentration, which is the solid volume per unit fluid volume or the solid mass per unit fluid volume.<br />
<br />
Observations show that the suspended sediment concentrations decrease with distance up from the bed. The rate of decrease depends on the ratio of the fall velocity <math>w_s</math> and the bed-shear velocity <math>u_*</math>. The depth-integrated suspended-load transport <math>q_{s,c}</math> is herein defined as the integration of the product of velocity <math>u</math> and concentration <math>c</math> from the edge of the bed-load layer, <math>z=a</math>, to the water surface, <math>z=h</math>.<br />
This definition requires the determination of the velocity profile, concentration profile and a known concentration <math>c_a</math> close to the bed (<math>z=a</math>), see Figure 4. These latter parameters are referred to as the reference concentration and the reference level.<br />
<br />
Sometimes, the suspended load transport is given as a mean volumetric concentration defined as the ratio of the volumetric suspended load transport (= sediment discharge) and the flow discharge <math>q</math>: <math>c_{mean}=q_{s,c}/q</math>. The mean concentration <math>c_{mean}</math> is approximately equal to the depth-averaged concentration for fine sediments (mud). <br />
<br />
The concentration can be expressed as a weight concentration <math>c_g</math> in kg/m3 or as a dimensionless volume concentration <math>c_v</math>. Sometimes the volume concentration is expressed as a volume percentage after multiplying with 100%.<br />
<br />
Some rivers carry very high concentrations of fine sediments (particles < 0.05 mm), usually referred to as the wash load. Experience shows that the presence of fines enhances the suspended sand transport rate because the fluid viscosity and density are increased by the fine sediments. As a result the fall velocity of the suspended sand particles will be reduced with respect to that in clear water and hence the suspended sand transport capacity of the flow will increase.<br />
<br />
The sediment concentration distribution over the water depth can be described as a diffusion process, which yields for steady, uniform flow <ref name=Rijn93></ref>: <br />
<br />
<math>c w_s + \varepsilon_s dc/dz = 0 , \qquad (8) </math> <br />
<br />
with <math>c</math> = sand concentration, <math>w_s</math> = particle fall velocity, <math>\varepsilon_s</math> = sediment diffusivity coefficient. <br />
<br />
Using a parabolic sediment diffusivity coefficient over the depth, the concentration profile can be expressed by the Rouse profile: <br />
<br />
<math>c(z)/c_a = [((h-z)/z) (a/(h-a))]^{w_s/\kappa u_*} , \qquad (9) </math><br />
<br />
with: <math>h</math> = water depth, <math>a</math> = reference level, <math>z</math> = height above bed, <br />
<math>c_a</math> = reference concentration, <br />
<br />
<math>w_s</math> = particle fall velocity, <math>u_*</math>= bed-shear velocity, <math>\kappa</math> = Von Karmann coefficient (=0.4).<br />
<br />
The relative importance of the suspended load transport is determined by the Rouse number <math>Z=w_s / \kappa u_*</math>. The following values can be used: <br />
<br />
<math>Z=5</math>: suspended sediment in near-bed layer (<math>z<0.1h</math>),<br />
<br />
<math>Z=2</math>: suspended sediment up to mid of water depth (<math>z<0.5h</math>),<br />
<br />
<math>Z=1</math>: suspended sediment up to water surface (<math>z<h</math>),<br />
<br />
<math>Z=0.1</math>: suspended sediment almost uniformly distributed over water depth.<br />
<br />
<br />
<br />
==Sand transport in non-steady (tidal) flow==<br />
<br />
In non-steady flow the actual sediment transport rate may be smaller (underload) or larger (overload) than the transport capacity resulting in net erosion or deposition assuming sufficient availability of bed material (no armour layers).<br />
<br />
Bed-load transport in non-steady flow can be modelled by a formula similar to steady flow because the adjustment of the transport of sediment particles close to the bed proceeds rapidly to the new hydraulic conditions.<br />
<br />
Suspended load transport, however, does not have such a behaviour because it takes time (time lag effects) to transport the particles upwards and downwards over the depth and therefore it is necessary to model the vertical convection-diffusion process.<br />
<br />
===Effect of time lag===<br />
<br />
[[Image:VanRijnFig6.jpg|thumb|500px|right|Figure 5: Time lag of suspended sediment concentration in tidal flow.]]<br />
<br />
Tidal flow is characterized by a daily ebb and flood cycle with a time scale of 6 to 12 hours (semidiurnal or diurnal tide) and by a neap-spring cycle with a time scale of about 14 days.<br />
Sediment concentration measurements in tidal flow over a fine sand bed (0.05 to 0.3 mm) show a continuous adjustment of the concentrations to the flow velocities with a lag period in the range of 0 to 60 minutes<br />
<br />
The basic transport process in tidal flow is shown in Figure 5. Sediment particles go into suspension when the current velocity exceeds a critical value. In accelerating flow there always is a net vertical upward transport of sediment particles due to turbulence-related diffusive processes, which continues as long as the sediment transport capacity exceeds the actual transport rate. The time lag period <math>\Delta T_1</math> is the time period between the time of maximum flow and the time at which the transport capacity is equal to the actual transport rate. After this latter time there is a net downward sediment transport because settling dominates yielding smaller concentrations and transport rates. In case of very fine sediments (silt) or a large depth, the settling process can continue during the slack water period giving a large time lag <math>\Delta T_2</math> which is defined as the period between the time of zero transport capacity and the start of a new erosion cycle. Figure 5 shows that the suspended sediment transport during decelerating flow is always larger than during accelerating flow.<br />
<br />
Time lag effects can be neglected for sediments larger than about 0.3 mm and hence a quasi-steady approach based on the available sediment transport formulas can be applied.<br />
<br />
===Effect of salinity stratification===<br />
<br />
In a stratified estuary a high-density salt wedge exists in the near-bed region resulting in relatively high near-bed densities and relatively low near-surface densities. Stratified flow will result in damping of turbulence because turbulence energy is consumed in the mixing of heavier fluid from a lower level to a higher level against the action of gravity.<br />
The usual method to account for the salinity-related stratification effect on the velocity and concentration profiles is the reduction of the fluid mixing coefficient, by introducing a damping factor related to the Richardson-number <math>Ri</math>, as follows: <math>\varepsilon_f = \phi \; \varepsilon_{f,0}</math> with <math>\varepsilon_{f,0}</math> = fluid mixing coefficient in fresh water, <math>\phi = F(Ri) </math> = damping factor (< 1), <math>Ri</math> = local Richardson number. The <math>\phi</math>-factor can be represented by a function given by Munk-Anderson<ref> Munk, W.H. and Anderson, E.R., 1948. Notes on the theory of the thermocline. Journal of Marine Research, Vol. 3, p 276-295.</ref>: <math> \phi = (1 + 3.3 Ri)^{-1.5}</math>.<br />
<br />
The simple sand transport formulas do not give realistic results when the salinity-related damping effect is significant (vertical density gradient in stratified flow).<br />
<br />
<br />
===Effect of mud===<br />
<br />
In most tidal basins the sediment bed consists of a mixture of sand and mud. The sand-mud mixture generally behaves as a mixture with cohesive properties when the mud fraction (all sediments < 0.05 mm) is dominant (> 0.3) and as a non-cohesive mixture when the sand fraction is dominant (> 0.7). The distinction between non-cohesive mixtures and cohesive mixtures can be related to a critical mud content (<math>p_{mud,cr}</math>). Most important is the value of the clay-fraction (sediments < 0.005 mm) in the mixture. Cohesive properties become dominant when the clay-fraction is larger than about 5% to 10%. Assuming a clay-mud ratio of 1/2 to 1/4 for natural mud beds, the critical mud content will be about <math>p_{mud,cr}= 0.2 - 0.4 .</math> <br />
If the mud content is below the critical value (<math>p_{mud} < p_{mud,cr}</math>), the sand-mud mixture can be assumed to be homogeneous with depth and to have non-cohesive properties. Furthermore, the erosion of the sand particles is the dominant erosion mechanism. The mud particles will be washed out together with the sand particles. Laboratory and field observations<ref name=Rijn93></ref> have shown that the erosion or pick-up process of the sand particles is slowed down by the presence of the mud particles. This behaviour can be quite well modelled by increasing the critical bed-shear stress for initiation of motion of the sand particles. Herein, it is assumed that: <math> \tau_{b,cr,sand} = (1+p_{mud})^{\beta} \tau_{b,cr,Shields}</math> with <math>\beta=3</math> based on analysis of field data. <br />
<br />
<br />
==Sand transport in non-steady coastal flows==<br />
<br />
Sand transport in a coastal environment generally occurs under the combined influence of a variety of hydrodynamic processes such as winds, waves and currents. <br />
<br />
Sand can be transported by wind-, wave-, tide- and density-driven currents (current-related or advective transport), by the oscillatory water motion itself (wave-related or oscillating transport) as caused by the deformation of short waves under the influence of decreasing water depth (wave asymmetry), or by a combination of currents and short waves. <br />
The waves generally act as sediment stirring agents; the sediments are transported by the mean current. Low-frequency waves interacting with short waves may also contribute to the sediment transport process. Wind-blown sand represents another basic transport process in the beach-dune zone.<br />
<br />
In friction-dominated deeper water outside the breaker (surf) zone the transport process is generally concentrated in a layer close to the sea bed; bed-load transport (bed form migration) and suspended transport may be equally important. Bed load type transport dominates in areas where the mean currents are relatively weak in comparison with the wave motion (small ratio of depth-averaged velocity and peak orbital velocity). Suspension of sediments can be caused by ripple-related vortices. The suspended load transport becomes increasingly important with increasing strength of the tide- and wind-driven mean current, due to the turbulence-related mixing capacity of the mean current (shearing in boundary layer). By this mechanism the sediments are mixed up from the bed-load layer to the upper layers of the flow.<br />
<br />
In the surf zone of sandy beaches the transport is generally dominated by waves through wave breaking and the associated wave-induced currents in the longshore and cross-shore directions. The longshore transport in the surf zone is also known as the longshore drift. The breaking process together with the near-bed wave-induced oscillatory water motion can bring relatively large quantities of sand into suspension (stirring) which is then transported as suspended load by net (wave-cycle averaged) currents such as tide-, wind- and density (salinity)-driven currents. The concentrations are generally maximum near the plunging point and decrease sharply on both sides of this location.<br />
<br />
The nature of the sea bed (plane or rippled bed) has a fundamental role in the transport of sediments by waves and currents. The configuration of the sea bed controls the near-bed velocity profile, the shear stresses and the turbulence and, thereby, the mixing and transport of the sediment particles. For example, the presence of ripples reduces near-bed velocities, but it enhances bed-shear stresses, turbulence and the entrainment of sediment particles, resulting in larger overall suspension levels. Several types of bed forms can be identified, depending on the type of wave-current motion and the bed material composition. Focusing on fine sand in the range of 0.1 to 0.3 mm, there is a sequence starting with the generation of rolling grain ripples, to vortex ripples and, finally, to upper plane bed with sheet flow for increasing bed-shear. Rolling grain ripples are low relief ripples that are formed just beyond the stage of initiation of motion. These ripples are transformed into more pronounced vortex ripples due to the generation of sediment-laden vortices formed in the lee of the ripple crests under increasing wave motion. The vortex ripples are washed out under large storm waves (in shallow water) resulting in plane bed sheet flow characterised by a thin layer of large sediment concentrations. <br />
<br />
<br />
==Simple general formulas for sand transport in rivers, estuaries and coastal waters==<br />
<br />
===Bed load transport===<br />
<br />
Van Rijn <ref>Van Rijn, L.C., 1984c. Sediment Transport, Part III: Bed Forms and Alluvial Roughness. Journal of Hydraulic Engineering, ASCE, Vol. 110, No. 12.</ref><ref name = Rijn93></ref><ref name=Rijn07a> Van Rijn, L.C., 2007. Unified view of sediment transport by currents and waves, I: Initiation of motion, bed roughness, and bed-load transport. Journal of Hydraulic Engineering, 133(6), p 649-667.</ref> proposed a simplified formula for bed-load transport <math>q_b</math> for combined steady current and waves, which reads as: <br />
<br />
<math>q_b = \alpha_b \rho_s U h (d_{50} / h )^{1.2} M_e^{1.5} , \qquad (10) </math> <br />
<br />
where<br />
<br />
<math>\alpha_b = 0.015</math>, <math>M_e = (U_e - U_{cr})/[(s-1)gd_{50}]^{0.5}</math> , <br />
<br />
<math>U_e = U+\gamma U_w</math> , with <math>\gamma=0.4</math> for irregular waves and <math>\gamma=0.8</math> for regular waves, <br />
<br />
<math>U</math> = wave- and depth-averaged flow velocity, <math>U_w = \pi H_s / [T_p \sinh(kh)]</math> = peak orbital velocity, <math>H_s</math> = significant wave height, <br />
<br />
<math>U_{cr} = \beta U_{cr,c} +(1-\beta) U_{cr,w}</math> = critical velocity, with <math>\beta = U / (U+U_w) </math> , <br />
<br />
<math>U_{cr,c}</math> = critical velocity for currents based on Shields <ref name=Rijn93></ref>, <math>U_{cr,w}</math> = critical velocity for waves <ref name=Rijn93></ref>, <br />
<br />
<math>U_{cr,c}= 0.19 d_{50}^{0.1} \log(4 h / d_{90})</math> for <math>0.0001<d_{50}<0.0005 \; m, </math> <br />
<br />
<math> U_{cr,c} = 8.5 d_{50}^{0.6} \log (4 h / d_{90})</math> for <math>0.0005<d_{50}<0.002 \; m</math> <br />
<br />
<math>U_{cr,w} = 0.24 [(s-1)g]^{0.66} d_{50}^{0.33} T_p^{0.33}</math> for <math>0.0001<d_{50}<0.0005 \; m,</math> <br />
<br />
<math>U_{cr,w} = 0.95 [(s-1)g]^{0.57} d_{50}^{0.43} T_p^{0.14}</math> for <math>0.0005<d_{50}<0.002 \; m.</math><br />
<br />
The inaccuracies are largest (underprediction) for relatively low <math>U_e</math> -velocities (<0.5 m/s) close to the critical velocities. Equation (6.1) describes the net bed load transport in current-dominated conditions (longshore flows). It cannot be used to compute the net cross-shore bed-load transport in the inner surf and swash zone. For these complicated conditions the full intra-wave method should be used, or other formulas such as given in [[Sediment transport formulas for the coastal environment]].<br />
<br />
===Suspended load transport===<br />
<br />
[[Image:VanRijnFig7.jpg|thumb|600px|right|Figure 6: Suspended transport as function of depth-averaged velocity.]]<br />
<br />
The simplified suspended load transport formula for steady flow proposed by Van Rijn<ref name=Rijn84>Van Rijn, L.C., 1984b. Sediment Transport, Part II: Suspended Load Transport. Journal of Hydraulic Engineering, ASCE, Vol. 110, No. 11.</ref> was extended to coastal flow (waves) and reads, as (see also Soulsby<ref name=Soul></ref>):<br />
<br />
<math> q_s = \alpha_s \rho_s U d_{50} M_e^{\eta} D_*^{-0.6} , \qquad (11) </math> <br />
<br />
with the same symbol definitions as for Eq. (10). <br />
<br />
According to the detailed TR2004 results <ref name=Rijn07b> Van Rijn, L.C., 2007. Unified view of sediment transport by currents and waves, II: Suspended transport. Journal of Hydraulic Engineering, 133(6), p 668-389.</ref>, the best matching values are <math>\alpha_s = 0.008</math> and <math>\eta = 2.4 .</math> <br />
<br />
Equation (11) defines the current-related suspended transport <math>q_s</math> which is the transport of sediment by the mean current including the effect of wave stirring on the sediment load. The suspended transport of very fine sediments (<0.1 mm) is somewhat underestimated. <br />
<br />
Equation (11) is based on the assumption that suspended load transport occurs for <math>U > U_{cr,motion}</math>, with <math>U_{cr,motion}</math> based on Equation (4). It is more physical to assume that suspended load transport occurs for <math>U > U_{cr,susp}</math> with <math>U_{cr,susp}</math> based on Equation (5). Using this latter approach, the suspended load transport is best represented by the parameters <math>\alpha_s=0.015</math> and <math>\eta=2</math>. <br />
<br />
Figure 6 shows both approaches for a water depth of <math>h= 5 \; m</math>, <math>d_{50} = 0.00025 \; m</math>. Measured transport rates (green trendline) based on the dataset given by Van Rijn <ref name=Rijn07b></ref> are also shown. Results are similar except for very small velocities < 0.5 m.<br />
<br />
<br />
===Sand transport computations for combined wave plus current conditions in water depth of 5 m===<br />
<br />
The detailed TR2004 model <ref name=Rijn07a></ref><ref name=Rijn07b></ref> was used to compute the total sand transport rates (bed load plus suspended load transport) for a depth of 5 m and a median size of <math>d_{50} = 0.00025 \; m \; (d_{10} = 0.000125 \; m, \; d_{90} = 0.0005 \; m).</math> The wave height was varied in the range of 0 to 3 m and wave periods in the range of 5 to 8 s. The wave direction is assumed to be normal to the coast, whereas the current is assumed to be parallel to the coast. <br />
<br />
[[Image:VanRijnFig8.jpg|thumb|600px|right|Figure 7: Total sand transport for combined wave plus current conditions, <math>h =5 \; m,</math> <math>d_{50} = 0.00025 \; m.</math>]]<br />
<br />
The total load transport (bed load + suspended load) results of the TR2004 model are shown in Figure 7 together with earlier results of the TR1993 model <ref name=Rijn93></ref> for the same parameter range. Some measured data of rivers and estuaries are also shown.<br />
The total sand transport based on the simplified formulae (Equations (10) and (11)) is also shown in Figure 7. <br />
Table 1 shows some values based on these equations with <math>\alpha_b = 0.015 , \alpha_s = 0.008</math> for <math>h = 5 \; m, v= 1 \; m/s,</math> <math>H_s = 0, 0.5, 1, 2, 3 \; m/s .</math><br />
It is noted that the transport rates are approximately equal for <math>H_s = 0 - 0.5 \; m</math> in the velocity range 1 - 2 m/s. Small waves of <math>H_s = 0.5 \; m</math> in a depth of 5 m have almost no effect on the sediment transport rate for velocities larger than about 1 m/s, because the current-related mixing is dominant. <br />
The TR2004 model yields slightly smaller values than the TR1993 model for the case without waves (<math>H_s = 0 \; m</math>). <br />
The TR2004 model yields considerably smaller (up to factor 3) total load transport rates for a steady current with high waves (<math>H_s = 3\; m</math>) compared to the results of the TR1993 model. This is mainly caused by the inclusion of a damping factor acting on the wave-related near-bed diffusivity in the upper regime with storm waves. <br />
The TR2004 results for steady flow (without waves) show reasonable agreement with measured values (data from major rivers and estuaries with depth of about 5 m and sediment size of about 0.00025 m) over the full velocity range from 0.6 - 2 m/s. <br />
<br />
The results of the TR2004 show that the total transport varies with <math>U^5</math> for <math>H_s = 0 \; m,</math> <math>U^{2.5}</math> for <math>H_s = 1\; m</math> and <math>U^2</math> for <math>H_s = 3\; m </math> <br />
The transport rate varies with <math>H_s^3</math> for <math>U = 0.5 \; m/s ,</math> with <math>H_s^{1.5}</math> for <math>U = 1 \; m/s</math> and with <math>H_s</math> for <math>U = 2 \; m/s .</math><br />
The total transport rate (<math>q_{tot}=q_b+q_s</math>) based on the simplified method generally are within a factor of 2 of the more detailed TR2004 model. The simplified method tend to underpredict for low and high velocities. <br />
<br />
<br />
<br />
[[Image:VanRijnTable1.jpg|thumb|700px|center|Table 1: Computed sand transport rates. Angle current-wave direction = <math>90^{\circ}</math>; Temperature = <math>15^{\circ}</math>Celsius, Salinity= 0 promille; <math>d_{50} = 0.25 \; mm, \; d_{90} = 0.5 \; mm.</math>]]<br />
<br />
<br />
==Related articles==<br />
<br />
[[Sediment transport formulas for the coastal environment]]<br />
<br />
[[Definitions, processes and models in morphology]]<br />
<br />
[[Bedforms and roughness]]<br />
<br />
[[Manual Sediment Transport Measurements in Rivers, Estuaries and Coastal Seas]]<br />
<br />
[[Coastal Hydrodynamics And Transport Processes]]<br />
<br />
[[Process-based morphological models]]<br />
<br />
[[Littoral drift and shoreline modelling]]<br />
<br />
<br />
<br />
==References==<br />
<br />
<references/><br />
<br />
<br />
<br />
{{author<br />
|AuthorID=13226 <br />
|AuthorFullName=Leo van Rijn<br />
|AuthorName=Leo van Rijn}}<br />
<br />
[[Category:Articles by Leo van Rijn]]<br />
[[Category:Physical coastal and marine processes]]<br />
[[Category:Sediment]]</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Sand_transport&diff=76338Sand transport2020-01-17T11:37:46Z<p>Dronkers J: </p>
<hr />
<div>SAND TRANSPORT<br />
<br />
<br />
==General characteristics==<br />
<br />
Sand can be transported by gravity-, wind-, wave-, tide- and density-driven currents (current-related transport), by the oscillatory water motion itself (wave-related transport) as caused by the deformation of short waves under the influence of decreasing water depth (wave asymmetry) or by a combination of currents and short waves. <br />
In rivers the gravity-induced flow generally is steady or quasi-steady generating bed load and suspended load transport of particles in conditions with an alluvial river bed. A typical feature of sediment transport along an alluvial bed is the generation of bed forms from small-scale ripples (order 0.1 m) up to large-scale dunes (order 100 m). The adjustment of large-scale bed forms such as dunes and sand waves may lead to non-steady effects (hysteresis effects) as it takes time for these large-scale features to adjust to changed flow conditions (flood waves). <br />
<br />
In the lower reaches of the river (estuary or tidal river) the influence of the tidal motion may introduce non-steady effects with varying current velocities and water levels on a diurnal or semi-diurnal time scale. Furthermore, density-induced flow may be generated due to the interaction of fresh river water and saline sea water (salt wedge). In coastal waters, sediment transport processes are strongly affected by high-frequency waves introducing oscillatory motions acting on the particles. The high-frequency (short) waves generally act as sediment stirring agents; net sediment transport is due to the mean current. <br />
<br />
Field experience over a long period of time in the coastal zone has led to the notion that storm waves cause sediments to move offshore while fair-weather waves and swell return the sediments shorewards. During conditions with low non-breaking waves, onshore-directed transport processes related to wave-asymmetry and wave-induced streaming are dominant, usually resulting in accretion processes in the beach zone. During high-energy conditions with breaking waves (storm cycles), the beach and dune zone of the coast are attacked severely by the incoming waves, usually resulting in erosion processes. <br />
<br />
<br />
==Definitions== <br />
<br />
Sand transport is herein defined as the transport of particles with sizes in the range of 0.05 to 2 mm as found in the bed of rivers, estuaries and coastal waters. The two main modes of sand transport are bed-load transport and suspended load transport. <br />
<br />
Bed-load transport is defined to consist of gliding, rolling and saltating particles in close contact with the bed and is dominated by flow-induced drag forces and by gravity forces acting on the particles. The suspended load transport is the irregular motion of the particles through the water column induced by turbulence-induced drag forces on the particles. Detailed information is presented by Van Rijn <ref name=Rijn93> Van Rijn, L.C., 1993, 2012. Principles of sediment transport in rivers, estuaries and coastal seas. Aqua Publications, Amsterdam, The Netherlands (WWW.AQUAPUBLICATIONS.NL)</ref>. The definition of bed-load transport is not universally agreed upon. Sheet flow transport at high bed-shear stresses may be considered as a type of bed-load transport, but it may also be seen as suspended load transport. Some regard bed-load transport as occurring in the region where concentrations are so high that grain-grain interactions are important, and grains are not supported purely by fluid forces. <br />
<br />
Suspended load transport can be determined by depth-integration of the product of sand concentration and fluid velocity from the top of the bed-load layer to the water surface. Herein, the net (averaged over the wave period) total sediment transport in coastal waters is defined as the vectorial sum of net the bed load <math>q_b</math> and net suspended load <math>q_s</math> transport rates: <br />
<br />
<math>q_{tot}=q_b+q_s</math>.<br />
<br />
For practical reasons, suspended transport in coastal waters will be subdivided into current-related and wave-related transport components. Thus, the suspended sand transport is represented as the vectorial sum of the current-related (<math>q_{s,c}</math> in current direction) and the wave-related (<math>q_{s,w}</math> in wave direction) transport components, as follows:<br />
<br />
<math>\vec q_s=\vec q_{s,c} + \vec q_{s,w}=\int \vec{v} cdz + \int <(\vec V - \vec v)(C-c)>dz , \qquad (1) </math> <br />
<br />
in which: <br />
<br />
<math>q_{s,c}</math> = time-averaged current-related suspended sediment transport rate,<br />
<br />
<math>q_{s,w}</math> = time-averaged wave-related suspended sediment transport rate (oscillating component), <br />
<br />
<math>v</math> = time-averaged velocity, <math>V</math> = instantaneous velocity, <br />
<br />
<math>C</math> = instantaneous concentration, <math>c</math> = time-averaged concentration, <br />
<br />
<math><f></math> represents averaging over time, <math> \int f dz</math> represents the integral from the top of the bed-load layer to the water surface. <br />
<br />
The precise definition of the lower limit of integration is of essential importance for accurate determination of the suspended transport rates. Furthermore, the velocity and concentration profiles must be known. <br />
<br />
The current-related suspended transport component <math>q_{s,c}</math> is defined as the advective transport of sediment particles by the time-averaged (mean) current velocities (longshore currents, rip currents, undertow currents); this component therefore represents the transport of sediment carried by the steady flow. <br />
In the case of waves superimposed on the current both the current velocities and the sediment concentrations will be affected by the wave motion. It is known that the wave motion reduces the current velocities near the bed while, in contrast, the near-bed concentrations are strongly increased due to the stirring action of the waves. These effects are included in the current-related transport. <br />
The wave-related suspended sediment transport <math>q_{s,w}</math> is defined as the transport of sediment particles by the high-frequency and low-frequency oscillating fluid components (cross-shore orbital motion). <br />
The suspended transport vector can be combined with the bed load transport vector to obtain the total transport vector: <math>q_{tot}</math>.<br />
<br />
In this note only the current-related bed load and suspended load transport components are considered. Usually, these components are dominant in river and tidal flows and also in wave-driven longshore flows.<br />
<br />
<br />
==Sand transport in steady river flow==<br />
<br />
===Basic characteristics===<br />
<br />
The transport of bed material particles may take place either as bed-load or as bed-load plus suspended load, depending on the size of the bed material particles and the flow conditions. The suspended load may also contain some wash load (usually, clay and silt particles smaller than 0.05 mm), which is generally defined as the portion of suspended load which is governed by the upstream supply rate and not by the composition and properties of the bed material. The wash load is mainly determined by land surface erosion (rainfall, no vegetation) and not by channel bed erosion. Although in natural conditions there is no sharp division between bed-load transport and suspended load transport, it is necessary to define a layer with bed-load transport for mathematical representation. <br />
<br />
When the value of the bed-shear velocity just exceeds the critical value for initiation of motion, the particles will be rolling and sliding or both, in continuous contact with the bed. For increasing values of the bed-shear velocity, the particles will be moving along the bed by more or less regular jumps, which is called saltation. When the value of the bed-shear velocity exceeds the fall velocity of the particles, the sediment particles can be lifted to a level at which the upward turbulent forces will be comparable with or of higher order than the submerged weight of the particles and as result the particles may go in suspension.<br />
<br />
The sediment transport in a steady uniform current over an alluvial bed is assumed to be equal to the transport capacity defined as the quantity of sediment that can be carried by the flow without net erosion or deposition, given sufficient availability of bed material (no armour layer). <br />
In general, a river flood wave is a relatively slow process with a time scale of a few days. Consequently, the sediment transport process in river flow can be represented as a quasi-steady process. Therefore, the available bed-load transport formulas and suspended load transport formulas can be applied for transport rate predictions. <br />
Flume and field data show that the sand transport rate is most strongly related to the depth-averaged velocity. The power of velocity is approximately 3 - 4. <br />
<br />
The bed material in natural conditions consists of non-uniform sediment particles. The effect of the non-uniformity of the sediments will result in selective transport processes (grain sorting). Grain sorting is related to the selective movement of sediment particles in a mixture near incipient motion at low bed-shear stresses and during generalized transport at higher shear stresses. Sorting effects can only be represented by taking the full size composition of the bed material, which may vary horizontally and vertically, into account. <br />
<br />
<br />
===Initiation of motion===<br />
<br />
[[Image:VanRijnFig1.jpg|thumb|500px|right|Figure 1: Initiation of motion according to Shields<ref name=Shields> Shields, A., 1936. Anwendung der Ähnlichkeitsmechanik und der Turbulenz Forschung auf die Geschiebebewegung. Mitt. der Preuss. Versuchsamst. für Wasserbau und Schiffbau, Heft 26, Berlin, Deutschland</ref> as function of Reynolds number.]]<br />
<br />
Particle movement will occur when the instantaneous fluid force on a particle is just larger than the instantaneous resisting force related to the submerged particle weight and the friction coefficient. The degree of exposure of a grain with respect to surrounding grains (hiding of smaller particles resting or moving between the larger particles) obviously is an important parameter determining the forces at initiation of motion. Cohesive forces are important when the bed consists of appreciable amounts of clay and silt particles.<br />
The driving forces are strongly related to the local near-bed velocities. In turbulent flow conditions the velocities are fluctuating in space and time. This makes together with the randomness of both particle size, shape and position that initiation of motion is not merely a deterministic phenomenon but a stochastic process as well.<br />
The fluid forces acting on a sediment particle resting on a horizontal bed consist of skin friction forces and pressure forces. The skin friction force acts on the surface of the particles by viscous shear. The pressure force consisting of a drag and a lift force is generated by pressure differences along the surface of the particle. These forces per unit bed surface area can be reformulated in a time-averaged bed-shear stress.<br />
<br />
Initiation of motion in steady flow is defined to occur when the dimensionless bed-shear stress <math>\theta</math> is larger than a threshold value <math>\theta_{cr}</math>. Thus, <math>\theta > \theta_{cr}</math> , with: <br />
<br />
<math>\theta = \tau_b / [(\rho_s-\rho_w) g d_{50}]</math> = Shields parameter, <math>d_{50}</math> = medium grain size, <math>\tau_b </math> = bed-shear stress, <br />
<br />
<math>\rho_s</math> = sediment density, <math>\rho_w</math> = fluid density, <math>d_{50} </math> = median sediment diameter.<br />
<br />
[[Image:VanRijnFig2.jpg|thumb|500px|right|Figure 2: Initiation of motion and suspension as function of dimensionless sediment size <math>D_*</math>.]]<br />
<br />
The <math>\theta_{cr}</math>- factor depends on the hydraulic conditions near the bed, the particle shape and the particle position relative to the other particles. The hydraulic conditions near the bed can be expressed by the Reynolds number <br />
<br />
<math>Re_* = u_* d/\nu</math>, where <br />
<br />
<math>u_*</math> = bed shear velocity , <math>d</math> = grain diameter, <math>\nu </math> = kinematic viscosity <math>(\sim 10^{-6}).</math> Thus: <math>\theta_{cr}= F(Re_*)</math> . <br />
<br />
Many experiments have been performed to determine the <math>\theta_{cr}</math>- values as a function of <math>Re_*</math>. The experimental results of Shields <ref name=Shields> </ref> related to a flat bed surface are most widely used to represent the critical conditions for initiation of motion (see Figure 1). The curve represents a critical stage at which only a minor part (say 1% to 10%) of the bed surface is moving.<br />
<br />
Initiation of motion in combined steady and oscillatory flow (wave motion) can also be expressed in terms of the Shields parameter or as function of a dimensionless particle size <math>D_*</math><ref name=Rijn93></ref>.<br />
<br />
The <math>D_*</math>-parameter is defined as: <br />
<br />
<math>D_*= [u_*d/(\nu \sqrt{\theta}]^{2/3} = d [(s-1) g / \nu^2]^{1/3}</math> , with:<br />
<br />
<math>g</math> = acceleration of gravity, <math>s = \rho_s/\rho_w</math> = relative density.<br />
<br />
A simple expression for initiation of motion (movement of particles along the bed) is given by Soulsby<ref name=Soul>Soulsby, R., 1997. Dynamics of marine sands. Thomas Telford, UK</ref>:<br />
<br />
<math> \theta_{cr,motion} = 0.3/(1+1.2 D_*) + 0.055 [1 - \exp(-0.02 D_*)] . \qquad (2) </math> . <br />
<br />
A simple expression for initiation of suspension (particles moving in suspension) is given by:<br />
<br />
<math> \theta_{cr,susp} = 0.3/(1+D_*) + 0.1 [1 - \exp(-0.05 D_*)] . \qquad (3) </math> . <br />
<br />
Equations (2) and (3) are shown in Figure 2.<br />
<br />
Both equations can be used to compute the critical depth-averaged velocity for initiation of motion and suspension, as follows:<br />
<br />
<math>U_{cr,motion} = 5.75 [\log(2h/d_{50})] [\theta_{cr,motion} (s-1) g d_{50}]^{0.5} , \qquad (4) </math> <br />
<br />
<math>U_{cr,susp} = 5.75 [\log(2h/d_{50})] [\theta_{cr, susp } (s-1) g d_{50}]^{0.5} , \qquad (5) </math> <br />
<br />
with: <math>U</math> = depth-averaged velocity, <math>C = 5.75 \sqrt{g} \log(4h/d_{90})</math> = Chézy coefficient, <br />
<br />
<math>h</math> = water depth, <math>d_{90} \approx 2d_{50}</math> = 90% particle size. <br />
<br />
Simple approximation formulas (10% accurate) are:<br />
<br />
<math>U_{cr,motion} = 0.19 (d_{50})^{0.1} \log(2h/d_{50})</math> for <math>0.0001<d_{50} < 0.0005 \; m ; </math><br />
<br />
<math>U_{cr,motion} = 8.5 (d_{50})^{0.6} \log(2h/d_{50})</math> for <math>0.0005<d_{50} < 0.002 \; m ; \qquad (6) </math> <br />
<br />
<math>U_{cr,susp} = 2.8 (h/d_{50})^{0.1} [(s-1) g d_{50}]^{0.5}</math> for <math>0.0001<d_{50} < 0.002 \; m . \qquad (7) </math> <br />
<br />
Figure 3 shows the critical depth-averaged velocities at initiation of motion and suspension for sediment with <math>d_{50}</math> between 0.1 and 2 mm based on Equations (4) and (5).<br />
<br />
[[Image:VanRijnFig3.jpg|thumb|600px|center|Figure 3: Depth-averaged velocity at initiation of motion and suspension.]]<br />
<br />
<br />
===Bed load transport===<br />
<br />
The transport of particles by rolling, sliding and saltating is known as bed-load transport. For example, Bagnold<ref> Bagnold, R.A., 1956. The Flow of Cohesionless Grains in Fluids. Proc. Royal Soc. Philos.Trans., London, Vol. 249.</ref> defines the bed-load transport as that in which the successive contacts of the particles with the bed are strictly limited by the effect of gravity, while the suspended-load transport is defined as that in which the excess weight of the particles is supported by random successions of upward impulses imported by turbulent eddies. Einstein<ref name=Einstein> Einstein, H.A., 1950. The Bed-Load Function for Sediment Transportation in Open Channel Flow. Technical Bulletin No. 1026, U.S. Dep. of Agriculture, Washington, D.C.</ref>, however, has a somewhat different approach. He defines the bed-load transport as the transport of sediment particles in a thin layer of 2 particle diameters thick just above the bed by sliding, rolling and sometimes by making jumps with a longitudinal distance of a few particle diameters. The bed layer is considered as a layer in which the mixing due to turbulence is so small that it cannot influence the sediment particles, and therefore suspension of particles is impossible in the bed-load layer. Further, Einstein assumes that the average distance travelled by any bed-load particle (as a series of successive movements) is a constant distance of 100 particle diameters, independent of the flow condition, the transport rate and the bed composition. In the view of Einstein, the saltating particles belong to the suspension mode of transport, because the jump lengths of saltating particles are considerably larger than a few grain diameters.<br />
<br />
The first reliable empirical bed load transport formula was presented by Meyer-Peter and Mueller<ref> Meyer-Peter, E. and Mueller, R., 1948. Formulas for Bed-Load Transport. Sec. Int. IAHR congress, Stockholm, Sweden.</ref>. They performed flume experiments with uniform particles and with particle mixtures. Based on data analysis, the following simple formula for bedload transport <math>q_b</math> was obtained, which is frequently used:<br />
<br />
<math>\Large\frac{q_b}{\sqrt{g (s-1) d_{50}^3}}\normalsize = m \, (\theta - \theta_{cr,motion})^n , </math><br />
<br />
where <math>s=\rho_s / \rho_w</math> and for <math>\theta_{cr,motion}</math> Eq. (2) can be used. For the dimensionless parameters <math>m</math> and <math>n</math> they advised the values <math>m=8</math> and <math>n=1.5</math>. In other studies a best fit to experimental data was found with values in the range <math>4<m<12</math> and <math>1.4<n<1.65</math>. <br />
<br />
Einstein<ref name=Einstein></ref> introduced statistical methods to represent the turbulent behaviour of the flow. Einstein gave a detailed but complicated statistical description of the particle motion in which the exchange probability of a particle is related to the hydrodynamic lift force and particle weight. Einstein proposed <math>d_{35}</math> as the effective diameter for particle mixtures and <math>d_{65}</math> as the effective diameter for grain roughness.<br />
<br />
Bagnold<ref> Bagnold, R.A., 1966. An Approach to the Sediment Transport Problem from General Physics. Geological Survey Prof. Paper 422-I, Washington.</ref> introduced an energy concept and related the sediment transport rate to the work done by the fluid.<br />
<br />
Engelund and Hansen<ref> Engelund, F. and Hansen, E., 1967. A Monograph on Sediment Transport in Alluvial Streams. Teknisk Forlag, Copenhagen, Denmark.</ref> presented a simple and reliable formula for the total load transport <math>q_{total}</math> in rivers:<br />
<br />
<math>\Large\frac{q_{total}}{\sqrt{g (s-1) d_{50}^3}}\normalsize = m \, \theta^{\, n} , </math><br />
<br />
with recommended values <math>n=2.5</math> and <math>m=0.04 / c_D</math>. The drag coefficient , which is defined as <math>c_D=\tau_b/(\rho u^2)</math>, is related to the Chezy coefficient <math>C \approx 5.75 \sqrt{g} \, \log_{10}(4 h / d_{90})</math> by <math>c_D=g/C^2</math>. This formula includes suspended load transport, but ignores phase lag effects of sediment suspension and settling. These phase lag effects can be important in non-steady flows. Therefore, in non-steady flows the Engelund-Hansen formula is not as accurate as total load formulas in which suspended load is computed with the formulas presented in the next sections.<br />
<br />
<br />
Van Rijn<ref> Van Rijn, L.C., 1984a. Sediment Transport, Part I: Bed Load Transport. Journal of Hydraulic Engineering, ASCE, Vol. 110, No. 10</ref> solved the equations of motions of an individual bed-load particle and computed the saltation characteristics and the particle velocity as a function of the flow conditions and the particle diameter for plane bed conditions. The results of sensitivity computations show that the bed load transport is only weakly affected by particle diameter. A 25%-variation of the particle diameter (<math>d_{50} = 0.8 \pm 0.2 \; mm</math>) results in a 10%-variation of the transport rate.<br />
<br />
Bed load transport <math>q_b</math> can be determined from the measured bed form dimensions and the measured bed form migration velocity using echo sounding results. The bed load transport is by definition: mass <math>m_s</math> per unit area of bed times migration velocity <math>c</math>: <math> q_b= c m_s </math>. <br />
The mass <math>M_s</math> of a triangular bed form with length <math>L</math>, height <math>\Delta H</math>, sediment density <math>\rho_s (\approx 2650 kg/m^3) </math> and porosity <math>p (\approx 0.4)</math> is <math>M_s = 0.5 \rho_s (1-p) L \Delta H </math>.<br />
The mass per unit area is the mass <math>M_s</math> divided by the length <math>L</math> giving <math>m_s = 0.5 \rho_s (1-p) \Delta H</math>. Bed load transport is thus given by: <br />
<br />
<math>q_b = 0.5 \rho_s (1-p)c \Delta H </math>.<br />
<br />
As bed forms are not fully triangular, a more general expression is: <br />
<br />
<math>q_b= \alpha \rho_s (1-p) c \Delta H </math>, with <math>\alpha = 0.5 - 0.7</math>.<br />
<br />
<br />
===Suspended load transport===<br />
<br />
[[Image:VanRijnFig5.jpg|thumb|500px|right|Figure 4: Definition sketch of suspended sediment transport.]]<br />
<br />
When the value of the bed-shear velocity exceeds the particle fall velocity, the particles can be lifted to a level at which the upward turbulent forces will be comparable to or higher than the submerged particle weight resulting in random particle trajectories due to turbulent velocity fluctuations. The particle velocity in longitudinal direction is almost equal to the fluid velocity. Usually, the behaviour of the suspended sediment particles is described in terms of the sediment concentration, which is the solid volume per unit fluid volume or the solid mass per unit fluid volume.<br />
<br />
Observations show that the suspended sediment concentrations decrease with distance up from the bed. The rate of decrease depends on the ratio of the fall velocity <math>w_s</math> and the bed-shear velocity <math>u_*</math>. The depth-integrated suspended-load transport <math>q_{s,c}</math> is herein defined as the integration of the product of velocity <math>u</math> and concentration <math>c</math> from the edge of the bed-load layer, <math>z=a</math>, to the water surface, <math>z=h</math>.<br />
This definition requires the determination of the velocity profile, concentration profile and a known concentration <math>c_a</math> close to the bed (<math>z=a</math>), see Figure 4. These latter parameters are referred to as the reference concentration and the reference level.<br />
<br />
Sometimes, the suspended load transport is given as a mean volumetric concentration defined as the ratio of the volumetric suspended load transport (= sediment discharge) and the flow discharge <math>q</math>: <math>c_{mean}=q_{s,c}/q</math>. The mean concentration <math>c_{mean}</math> is approximately equal to the depth-averaged concentration for fine sediments (mud). <br />
<br />
The concentration can be expressed as a weight concentration <math>c_g</math> in kg/m3 or as a dimensionless volume concentration <math>c_v</math>. Sometimes the volume concentration is expressed as a volume percentage after multiplying with 100%.<br />
<br />
Some rivers carry very high concentrations of fine sediments (particles < 0.05 mm), usually referred to as the wash load. Experience shows that the presence of fines enhances the suspended sand transport rate because the fluid viscosity and density are increased by the fine sediments. As a result the fall velocity of the suspended sand particles will be reduced with respect to that in clear water and hence the suspended sand transport capacity of the flow will increase.<br />
<br />
The sediment concentration distribution over the water depth can be described as a diffusion process, which yields for steady, uniform flow <ref name=Rijn93></ref>: <br />
<br />
<math>c w_s + \varepsilon_s dc/dz = 0 , \qquad (8) </math> <br />
<br />
with <math>c</math> = sand concentration, <math>w_s</math> = particle fall velocity, <math>\varepsilon_s</math> = sediment diffusivity coefficient. <br />
<br />
Using a parabolic sediment diffusivity coefficient over the depth, the concentration profile can be expressed by the Rouse profile: <br />
<br />
<math>c(z)/c_a = [((h-z)/z) (a/(h-a))]^{w_s/\kappa u_*} , \qquad (9) </math><br />
<br />
with: <math>h</math> = water depth, <math>a</math> = reference level, <math>z</math> = height above bed, <br />
<math>c_a</math> = reference concentration, <br />
<br />
<math>w_s</math> = particle fall velocity, <math>u_*</math>= bed-shear velocity, <math>\kappa</math> = Von Karmann coefficient (=0.4).<br />
<br />
The relative importance of the suspended load transport is determined by the Rouse number <math>Z=w_s / \kappa u_*</math>. The following values can be used: <br />
<br />
<math>Z=5</math>: suspended sediment in near-bed layer (<math>z<0.1h</math>),<br />
<br />
<math>Z=2</math>: suspended sediment up to mid of water depth (<math>z<0.5h</math>),<br />
<br />
<math>Z=1</math>: suspended sediment up to water surface (<math>z<h</math>),<br />
<br />
<math>Z=0.1</math>: suspended sediment almost uniformly distributed over water depth.<br />
<br />
<br />
<br />
==Sand transport in non-steady (tidal) flow==<br />
<br />
In non-steady flow the actual sediment transport rate may be smaller (underload) or larger (overload) than the transport capacity resulting in net erosion or deposition assuming sufficient availability of bed material (no armour layers).<br />
<br />
Bed-load transport in non-steady flow can be modelled by a formula similar to steady flow because the adjustment of the transport of sediment particles close to the bed proceeds rapidly to the new hydraulic conditions.<br />
<br />
Suspended load transport, however, does not have such a behaviour because it takes time (time lag effects) to transport the particles upwards and downwards over the depth and therefore it is necessary to model the vertical convection-diffusion process.<br />
<br />
===Effect of time lag===<br />
<br />
[[Image:VanRijnFig6.jpg|thumb|500px|right|Figure 5: Time lag of suspended sediment concentration in tidal flow.]]<br />
<br />
Tidal flow is characterized by a daily ebb and flood cycle with a time scale of 6 to 12 hours (semidiurnal or diurnal tide) and by a neap-spring cycle with a time scale of about 14 days.<br />
Sediment concentration measurements in tidal flow over a fine sand bed (0.05 to 0.3 mm) show a continuous adjustment of the concentrations to the flow velocities with a lag period in the range of 0 to 60 minutes<br />
<br />
The basic transport process in tidal flow is shown in Figure 5. Sediment particles go into suspension when the current velocity exceeds a critical value. In accelerating flow there always is a net vertical upward transport of sediment particles due to turbulence-related diffusive processes, which continues as long as the sediment transport capacity exceeds the actual transport rate. The time lag period <math>\Delta T_1</math> is the time period between the time of maximum flow and the time at which the transport capacity is equal to the actual transport rate. After this latter time there is a net downward sediment transport because settling dominates yielding smaller concentrations and transport rates. In case of very fine sediments (silt) or a large depth, the settling process can continue during the slack water period giving a large time lag <math>\Delta T_2</math> which is defined as the period between the time of zero transport capacity and the start of a new erosion cycle. Figure 5 shows that the suspended sediment transport during decelerating flow is always larger than during accelerating flow.<br />
<br />
Time lag effects can be neglected for sediments larger than about 0.3 mm and hence a quasi-steady approach based on the available sediment transport formulas can be applied.<br />
<br />
===Effect of salinity stratification===<br />
<br />
In a stratified estuary a high-density salt wedge exists in the near-bed region resulting in relatively high near-bed densities and relatively low near-surface densities. Stratified flow will result in damping of turbulence because turbulence energy is consumed in the mixing of heavier fluid from a lower level to a higher level against the action of gravity.<br />
The usual method to account for the salinity-related stratification effect on the velocity and concentration profiles is the reduction of the fluid mixing coefficient, by introducing a damping factor related to the Richardson-number <math>Ri</math>, as follows: <math>\varepsilon_f = \phi \; \varepsilon_{f,0}</math> with <math>\varepsilon_{f,0}</math> = fluid mixing coefficient in fresh water, <math>\phi = F(Ri) </math> = damping factor (< 1), <math>Ri</math> = local Richardson number. The <math>\phi</math>-factor can be represented by a function given by Munk-Anderson<ref> Munk, W.H. and Anderson, E.R., 1948. Notes on the theory of the thermocline. Journal of Marine Research, Vol. 3, p 276-295.</ref>: <math> \phi = (1 + 3.3 Ri)^{-1.5}</math>.<br />
<br />
The simple sand transport formulas do not give realistic results when the salinity-related damping effect is significant (vertical density gradient in stratified flow).<br />
<br />
<br />
===Effect of mud===<br />
<br />
In most tidal basins the sediment bed consists of a mixture of sand and mud. The sand-mud mixture generally behaves as a mixture with cohesive properties when the mud fraction (all sediments < 0.05 mm) is dominant (> 0.3) and as a non-cohesive mixture when the sand fraction is dominant (> 0.7). The distinction between non-cohesive mixtures and cohesive mixtures can be related to a critical mud content (<math>p_{mud,cr}</math>). Most important is the value of the clay-fraction (sediments < 0.005 mm) in the mixture. Cohesive properties become dominant when the clay-fraction is larger than about 5% to 10%. Assuming a clay-mud ratio of 1/2 to 1/4 for natural mud beds, the critical mud content will be about <math>p_{mud,cr}= 0.2 - 0.4 .</math> <br />
If the mud content is below the critical value (<math>p_{mud} < p_{mud,cr}</math>), the sand-mud mixture can be assumed to be homogeneous with depth and to have non-cohesive properties. Furthermore, the erosion of the sand particles is the dominant erosion mechanism. The mud particles will be washed out together with the sand particles. Laboratory and field observations<ref name=Rijn93></ref> have shown that the erosion or pick-up process of the sand particles is slowed down by the presence of the mud particles. This behaviour can be quite well modelled by increasing the critical bed-shear stress for initiation of motion of the sand particles. Herein, it is assumed that: <math> \tau_{b,cr,sand} = (1+p_{mud})^{\beta} \tau_{b,cr,Shields}</math> with <math>\beta=3</math> based on analysis of field data. <br />
<br />
<br />
==Sand transport in non-steady coastal flows==<br />
<br />
Sand transport in a coastal environment generally occurs under the combined influence of a variety of hydrodynamic processes such as winds, waves and currents. <br />
<br />
Sand can be transported by wind-, wave-, tide- and density-driven currents (current-related or advective transport), by the oscillatory water motion itself (wave-related or oscillating transport) as caused by the deformation of short waves under the influence of decreasing water depth (wave asymmetry), or by a combination of currents and short waves. <br />
The waves generally act as sediment stirring agents; the sediments are transported by the mean current. Low-frequency waves interacting with short waves may also contribute to the sediment transport process. Wind-blown sand represents another basic transport process in the beach-dune zone.<br />
<br />
In friction-dominated deeper water outside the breaker (surf) zone the transport process is generally concentrated in a layer close to the sea bed; bed-load transport (bed form migration) and suspended transport may be equally important. Bed load type transport dominates in areas where the mean currents are relatively weak in comparison with the wave motion (small ratio of depth-averaged velocity and peak orbital velocity). Suspension of sediments can be caused by ripple-related vortices. The suspended load transport becomes increasingly important with increasing strength of the tide- and wind-driven mean current, due to the turbulence-related mixing capacity of the mean current (shearing in boundary layer). By this mechanism the sediments are mixed up from the bed-load layer to the upper layers of the flow.<br />
<br />
In the surf zone of sandy beaches the transport is generally dominated by waves through wave breaking and the associated wave-induced currents in the longshore and cross-shore directions. The longshore transport in the surf zone is also known as the longshore drift. The breaking process together with the near-bed wave-induced oscillatory water motion can bring relatively large quantities of sand into suspension (stirring) which is then transported as suspended load by net (wave-cycle averaged) currents such as tide-, wind- and density (salinity)-driven currents. The concentrations are generally maximum near the plunging point and decrease sharply on both sides of this location.<br />
<br />
The nature of the sea bed (plane or rippled bed) has a fundamental role in the transport of sediments by waves and currents. The configuration of the sea bed controls the near-bed velocity profile, the shear stresses and the turbulence and, thereby, the mixing and transport of the sediment particles. For example, the presence of ripples reduces near-bed velocities, but it enhances bed-shear stresses, turbulence and the entrainment of sediment particles, resulting in larger overall suspension levels. Several types of bed forms can be identified, depending on the type of wave-current motion and the bed material composition. Focusing on fine sand in the range of 0.1 to 0.3 mm, there is a sequence starting with the generation of rolling grain ripples, to vortex ripples and, finally, to upper plane bed with sheet flow for increasing bed-shear. Rolling grain ripples are low relief ripples that are formed just beyond the stage of initiation of motion. These ripples are transformed into more pronounced vortex ripples due to the generation of sediment-laden vortices formed in the lee of the ripple crests under increasing wave motion. The vortex ripples are washed out under large storm waves (in shallow water) resulting in plane bed sheet flow characterised by a thin layer of large sediment concentrations. <br />
<br />
<br />
==Simple general formulas for sand transport in rivers, estuaries and coastal waters==<br />
<br />
===Bed load transport===<br />
<br />
Van Rijn <ref>Van Rijn, L.C., 1984c. Sediment Transport, Part III: Bed Forms and Alluvial Roughness. Journal of Hydraulic Engineering, ASCE, Vol. 110, No. 12.</ref><ref name = Rijn93></ref><ref name=Rijn07a> Van Rijn, L.C., 2007. Unified view of sediment transport by currents and waves, I: Initiation of motion, bed roughness, and bed-load transport. Journal of Hydraulic Engineering, 133(6), p 649-667.</ref> proposed a simplified formula for bed-load transport <math>q_b</math> for combined steady current and waves, which reads as: <br />
<br />
<math>q_b = \alpha_b \rho_s U h (d_{50} / h )^{1.2} M_e^{1.5} , \qquad (10) </math> <br />
<br />
where<br />
<br />
<math>\alpha_b = 0.015</math>, <math>M_e = (U_e - U_{cr})/[(s-1)gd_{50}]^{0.5}</math> , <br />
<br />
<math>U_e = U+\gamma U_w</math> , with <math>\gamma=0.4</math> for irregular waves and <math>\gamma=0.8</math> for regular waves, <br />
<br />
<math>U</math> = wave- and depth-averaged flow velocity, <math>U_w = \pi H_s / [T_p \sinh(kh)]</math> = peak orbital velocity, <math>H_s</math> = significant wave height, <br />
<br />
<math>U_{cr} = \beta U_{cr,c} +(1-\beta) U_{cr,w}</math> = critical velocity, with <math>\beta = U / (U+U_w) </math> , <br />
<br />
<math>U_{cr,c}</math> = critical velocity for currents based on Shields <ref name=Rijn93></ref>, <math>U_{cr,w}</math> = critical velocity for waves <ref name=Rijn93></ref>, <br />
<br />
<math>U_{cr,c}= 0.19 d_{50}^{0.1} \log(4 h / d_{90})</math> for <math>0.0001<d_{50}<0.0005 \; m, </math> <br />
<br />
<math> U_{cr,c} = 8.5 d_{50}^{0.6} \log (4 h / d_{90})</math> for <math>0.0005<d_{50}<0.002 \; m</math> <br />
<br />
<math>U_{cr,w} = 0.24 [(s-1)g]^{0.66} d_{50}^{0.33} T_p^{0.33}</math> for <math>0.0001<d_{50}<0.0005 \; m,</math> <br />
<br />
<math>U_{cr,w} = 0.95 [(s-1)g]^{0.57} d_{50}^{0.43} T_p^{0.14}</math> for <math>0.0005<d_{50}<0.002 \; m.</math><br />
<br />
The inaccuracies are largest (underprediction) for relatively low <math>U_e</math> -velocities (<0.5 m/s) close to the critical velocities. Equation (6.1) describes the net bed load transport in current-dominated conditions (longshore flows). It cannot be used to compute the net cross-shore bed-load transport in the inner surf and swash zone. For these complicated conditions the full intra-wave method should be used, or other formulas such as given in [[Sediment transport formulas for the coastal environment]].<br />
<br />
===Suspended load transport===<br />
<br />
[[Image:VanRijnFig7.jpg|thumb|600px|right|Figure 6: Suspended transport as function of depth-averaged velocity.]]<br />
<br />
The simplified suspended load transport formula for steady flow proposed by Van Rijn<ref name=Rijn84>Van Rijn, L.C., 1984b. Sediment Transport, Part II: Suspended Load Transport. Journal of Hydraulic Engineering, ASCE, Vol. 110, No. 11.</ref> was extended to coastal flow (waves) and reads, as (see also Soulsby<ref name=Soul></ref>):<br />
<br />
<math> q_s = \alpha_s \rho_s U d_{50} M_e^{\eta} D_*^{-0.6} , \qquad (11) </math> <br />
<br />
with the same symbol definitions as for Eq. (10). <br />
<br />
According to the detailed TR2004 results <ref name=Rijn07b> Van Rijn, L.C., 2007. Unified view of sediment transport by currents and waves, II: Suspended transport. Journal of Hydraulic Engineering, 133(6), p 668-389.</ref>, the best matching values are <math>\alpha_s = 0.008</math> and <math>\eta = 2.4 .</math> <br />
<br />
Equation (11) defines the current-related suspended transport <math>q_s</math> which is the transport of sediment by the mean current including the effect of wave stirring on the sediment load. The suspended transport of very fine sediments (<0.1 mm) is somewhat underestimated. <br />
<br />
Equation (11) is based on the assumption that suspended load transport occurs for <math>U > U_{cr,motion}</math>, with <math>U_{cr,motion}</math> based on Equation (4). It is more physical to assume that suspended load transport occurs for <math>U > U_{cr,susp}</math> with <math>U_{cr,susp}</math> based on Equation (5). Using this latter approach, the suspended load transport is best represented by the parameters <math>\alpha_s=0.015</math> and <math>\eta=2</math>. <br />
<br />
Figure 6 shows both approaches for a water depth of <math>h= 5 \; m</math>, <math>d_{50} = 0.00025 \; m</math>. Measured transport rates (green trendline) based on the dataset given by Van Rijn <ref name=Rijn07b></ref> are also shown. Results are similar except for very small velocities < 0.5 m.<br />
<br />
<br />
===Sand transport computations for combined wave plus current conditions in water depth of 5 m===<br />
<br />
The detailed TR2004 model <ref name=Rijn07a></ref><ref name=Rijn07b></ref> was used to compute the total sand transport rates (bed load plus suspended load transport) for a depth of 5 m and a median size of <math>d_{50} = 0.00025 \; m \; (d_{10} = 0.000125 \; m, \; d_{90} = 0.0005 \; m).</math> The wave height was varied in the range of 0 to 3 m and wave periods in the range of 5 to 8 s. The wave direction is assumed to be normal to the coast, whereas the current is assumed to be parallel to the coast. <br />
<br />
[[Image:VanRijnFig8.jpg|thumb|600px|right|Figure 7: Total sand transport for combined wave plus current conditions, <math>h =5 \; m,</math> <math>d_{50} = 0.00025 \; m.</math>]]<br />
<br />
The total load transport (bed load + suspended load) results of the TR2004 model are shown in Figure 7 together with earlier results of the TR1993 model <ref name=Rijn93></ref> for the same parameter range. Some measured data of rivers and estuaries are also shown.<br />
The total sand transport based on the simplified formulae (Equations (10) and (11)) is also shown in Figure 7. <br />
Table 1 shows some values based on these equations with <math>\alpha_b = 0.015 , \alpha_s = 0.008</math> for <math>h = 5 \; m, v= 1 \; m/s,</math> <math>H_s = 0, 0.5, 1, 2, 3 \; m/s .</math><br />
It is noted that the transport rates are approximately equal for <math>H_s = 0 - 0.5 \; m</math> in the velocity range 1 - 2 m/s. Small waves of <math>H_s = 0.5 \; m</math> in a depth of 5 m have almost no effect on the sediment transport rate for velocities larger than about 1 m/s, because the current-related mixing is dominant. <br />
The TR2004 model yields slightly smaller values than the TR1993 model for the case without waves (<math>H_s = 0 \; m</math>). <br />
The TR2004 model yields considerably smaller (up to factor 3) total load transport rates for a steady current with high waves (<math>H_s = 3\; m</math>) compared to the results of the TR1993 model. This is mainly caused by the inclusion of a damping factor acting on the wave-related near-bed diffusivity in the upper regime with storm waves. <br />
The TR2004 results for steady flow (without waves) show reasonable agreement with measured values (data from major rivers and estuaries with depth of about 5 m and sediment size of about 0.00025 m) over the full velocity range from 0.6 - 2 m/s. <br />
<br />
The results of the TR2004 show that the total transport varies with <math>U^5</math> for <math>H_s = 0 \; m,</math> <math>U^{2.5}</math> for <math>H_s = 1\; m</math> and <math>U^2</math> for <math>H_s = 3\; m </math> <br />
The transport rate varies with <math>H_s^3</math> for <math>U = 0.5 \; m/s ,</math> with <math>H_s^{1.5}</math> for <math>U = 1 \; m/s</math> and with <math>H_s</math> for <math>U = 2 \; m/s .</math><br />
The total transport rate (<math>q_{tot}=q_b+q_s</math>) based on the simplified method generally are within a factor of 2 of the more detailed TR2004 model. The simplified method tend to underpredict for low and high velocities. <br />
<br />
<br />
<br />
[[Image:VanRijnTable1.jpg|thumb|700px|center|Table 1: Computed sand transport rates. Angle current-wave direction = <math>90^{\circ}</math>; Temperature = <math>15^{\circ}</math>Celsius, Salinity= 0 promille; <math>d_{50} = 0.25 \; mm, \; d_{90} = 0.5 \; mm.</math>]]<br />
<br />
<br />
==Related articles==<br />
<br />
[[Sediment transport formulas for the coastal environment]]<br />
<br />
[[Definitions, processes and models in morphology]]<br />
<br />
[[Bedforms and roughness]]<br />
<br />
[[Manual Sediment Transport Measurements in Rivers, Estuaries and Coastal Seas]]<br />
<br />
[[Coastal Hydrodynamics And Transport Processes]]<br />
<br />
[[Process-based morphological models]]<br />
<br />
[[Littoral drift and shoreline modelling]]<br />
<br />
<br />
<br />
==References==<br />
<br />
<references/><br />
<br />
<br />
<br />
{{author<br />
|AuthorID=13226 <br />
|AuthorFullName=Leo van Rijn<br />
|AuthorName=Leo van Rijn}}<br />
<br />
[[Category:Articles by Leo van Rijn]]<br />
[[Category:Physical coastal and marine processes]]<br />
[[Category:Sediment]]</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Bed_roughness_and_friction_factors_in_estuaries&diff=76337Bed roughness and friction factors in estuaries2020-01-17T11:08:25Z<p>Dronkers J: </p>
<hr />
<div>==Introduction==<br />
<br />
Water movements in an estuary are driven by gravity, through water-level gradients induced by tides, wind and river discharge and through density gradients. Momentum is dissipated along the course of the flow because of a number of reasons: friction of the water against the bed and the banks, irregularities of the bed (so-called “bedforms”), channel bends, turbulence, density currents, sediment transport, friction at the free surface, waves, irregularities of the cross section, groins, sills, ... Not all of these phenomena are accounted for individually and explicitly in operational models.<br />
<br />
==1D models==<br />
<br />
In 1D models, the equations describing the flow are the continuity equation (mass conservation) and momentum conservation :<br />
<br />
<math> \frac{\partial h}{\partial t} + \frac{\partial hu}{\partial x} =0 , </math><br />
<br />
<math> \frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} + g \frac{\partial (z_b+h)}{\partial x} = -W , </math><br />
<br />
in which <math>h(x,t)</math> is the mean water depth in a cross section,<br />
<math>u(x,t)</math> the mean velocity averaged over the cross section,<br />
<math>x</math> is the distance along the estuary,<br />
<math>z_b</math> the bed level relative to a horizontal datum,<br />
<math>t</math> is time, <math>\rho</math> the water density <br />
and <math>g</math> is the gravity acceleration.<br />
<br />
<math>W</math> is the resistance term or momentum loss per unit weight of water. <math>W</math> is assumed to be caused mainly by bottom friction and is expressed as a bed shear stress <math>\tau</math> divided by the hydraulic radius <math>R,</math><br />
<br />
<math> W = \frac{\tau}{\rho R} . </math><br />
<br />
The hydraulic radius is given by the ratio cross-section to wetted perimeter; in wide shallow estuaries it is approximately equal to the water depth <math>h.</math><br />
The bed shear stress is related to the velocity <math>u</math> by a dimensionless friction factor <math>c_D</math>,<br />
<br />
<math> \tau = c_D \rho u^2 .</math><br />
<br />
The bottom friction factor <math>c_D</math> incorporates all flow resisting effects and therefore has no well-defined physical meaning.<br />
Instead of <math>c_D</math>, sometimes the Chezy coefficient <math>C \; [m^{1/2} s^{-1}]</math> is used as friction factor; it is related to <math>c_D</math> by <math>C=\sqrt{g/c_D}.</math><br />
<br />
The friction factor is not a constant but (even in the absence of other drag forces than friction) depends for example on the water depth. It can (for a particular cross section or a “homogenous” river stretch) be calculated by an empirical formula e.g. Manning-Strickler or by the semi-empirical White-Colebrook formula. For estuaries, typical values of <math>c_D</math> are in the range 0.001-0.004.<br />
<br />
==Manning-Strickler formula==<br />
<br />
The Manning-Strickler formula for the friction coefficient introduces an explicit dependence on the depth <math>h</math>:<br />
<br />
<math>c_D = g n^2 h^{-1/3}= g K^{-2} h^{-1/3} , </math><br />
<br />
in which <math>n</math> is the Manning coefficient and <math>K</math> the Strickler coefficient.<br />
Strickler-type equations (quadratic friction laws) are applicable to wide-shallow channels (width-depth ratio greater than 10) where the hydraulic radius can be replaced by the mean depth.<br />
<br />
For granular beds and in the absence of bedforms, the Manning (Strickler) coefficient can be estimated by <ref> Ackers, P. and White, W.R. (1973) Sediment Transport: New Approach and Analysis. Journal of the Hydraulics Division, ASCE, No. HY11</ref>:<br />
<math> n = 1/K = (0.04 - 0.047) \times d_{90}^{1.6} , </math><br />
where <math>d_{90}</math> is the <math>90\%</math> grain diameter of the bed material (<math>90\%</math> is finer).<br />
<br />
==White-Colebrook (Thysse) equation==<br />
<br />
For large Reynolds numbers - the case of estuaries - the empirical White-Colebrook reads <ref> ASCE Task Force on Friction Factors in Open Channels (1963) Friction factors in open channels. J. Hydraulics Div. ASCE 89: 97–143</ref><br />
<br />
<math> c_D \approx 0.03 \left[ log_{10} \left( \frac{k_s}{12 h} \right) \right]^{-2} . </math><br />
<br />
Here is <math>k_s</math> [m] the roughness height, which is of the order of <math>d_{90}</math>. Sometimes one assumes <math>k_s \approx 3 d_{50} .</math><br />
<br />
Since the friction factor includes all other flow resistances, <math>n</math> or <math>k_s</math> is not a real physical parameter but rather a calibration parameter. '''Calibration''' is done by trial and error, by comparing computed water surface profiles with measured water surface profiles (maregraph stations or limnigraphs along the estuary). A different data set should be used for the '''validation''' of the roughness model.<br />
The ‘overall’ quality of the calibration/ validation is measured by statistical methods as there are: RMSE, standard deviation, or the percentage of time that the deviation between the measurement and the model remains within a chosen accuracy margin.<br />
<br />
In case of a sinusoidal velocity, <math> u = U \cos ( 2 \pi t/T) </math>, the quadratic friction is sometimes replaced by an equivalent linear friction term<br />
<br />
<math> W = r \frac{u}{ h} </math> with <math>r \approx \frac{ 8 c_D}{3 \pi} U .</math><br />
<br />
<br />
==2D models==<br />
<br />
In 2D models, the governing equations are (conservation of momentum and mass)<br />
<br />
<math> \frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y} + g \frac{\partial \eta}{\partial x} - fv = - c_D \frac{u (u^2+v^2)^{1/2}}{h} + c_W \frac{W^2 \cos \theta}{h} + N_1 \Delta u , </math><br />
<br />
<math> \frac{\partial v}{\partial t} + u \frac{\partial v}{\partial x} + v \frac{\partial v}{\partial y} + g \frac{\partial \eta}{\partial y} + fu = - c_D \frac{v (u^2+v^2)^{1/2}}{h} + c_W \frac{W^2 \sin \theta}{h} + N_2 \Delta v , </math><br />
<br />
<math> \frac{\partial \eta}{\partial t} + \frac{\partial hu}{\partial x} + \frac{\partial hv}{\partial y} =0 . </math><br />
<br />
These are the so called “de St. Venant equations” or “shallow water equations”, in which<br />
<math>\eta(x,y,t)</math> is the water level relative to a horizontal datum,<br />
<math>u(x,y,t), v(x,y,t)</math> are the <math>x,y</math>-components of the current velocity,<br />
<math>f</math> is the Coriolis parameter (at <math>51^0</math> latitude <math>f= 1.13 10^{-4} s^{-1}</math>),<br />
<math>c_W</math> the surface friction factor due to wind,<br />
<math>W</math> the wind velocity, <math>\theta</math> the wind angle.<br />
The kinematic turbulent diffusion coefficients <math>N_1, N_2 </math> should be calculated by an appropriate turbulence model, for example: constant eddy viscosity, mixing length model (diffusion coefficients depending on the scale of the vortices that can develop) or <math>k-\epsilon</math> model (introducing additional equations for turbulent kinetic energy <math>k</math> and turbulent energy dissipation <math>\epsilon</math> <ref>Launder, B.E. and Spalding, D.B. (1974) The numerical computation of turbulent flows. Computer Methods in Applied Mechanics and Engineering 3: 269–289</ref>). In 2D and 3D models, the use of <math>k-\epsilon</math> is state of the art. <br />
The actual value of <math>c_D</math> depends on the bed roughness, which may be decomposed into two parts (see also [[Bedforms and roughness]]): <br />
* Skin friction or surface drag, which is mainly a function of the bed roughness or the diameter of the grains that compose the bed; <math>c_D</math> is either assumed to be a constant in a particular section or stretch of the estuary or calculated by an empirical formula e.g. Manning - Strickler or by the White-Colebrook formula.<br />
* Form drag or form roughness (bar or shape resistance), which is caused by the presence of bedforms on the bottom of the estuary. Bedforms may vary between small ripples (with a height which is a few orders of magnitude smaller than the water depth) and mega-ripples or dunes (with a height of the same order of magnitude as the water depth). Their formation and appearance is a function of the flow velocity (incl. the effect of waves) and varies from place to place and with time (a.o. as a function of river discharge or the presence of mud).<br />
The flow resistance due to form roughness can be calculated with a White-Colebrook type equation. For currents only, the ripple bed roughness (<math>k_r</math>) is a function of the mobility number <math>\psi = \rho (u^2+v^2)/(g d_{50} \Delta \rho ) </math>, where <math>\Delta \rho</math> is the sediment-water density difference <ref> Van Rijn, L. (2007) Unified View of Sediment Transport by Currents and Waves. I: Initiation of Motion, Bed Roughness, and Bed-Load Transport. Journal of Hydraulic Engineering ASCE 133: 649-667</ref>:<br />
<br />
<math> k_r = d_{50} \left(85-65 \tanh[0.015(\psi-150)]\right) , \; \psi < 250 ; \quad k_r=20 d_{50}, \; \psi \leq 250 .</math><br />
<br />
Calibration takes into account all the other neglected drag forces; <math>c_D</math> (or <math>n</math> or <math>K</math>) then basically becomes a calibration parameter. Calibration of the friction factor is done by comparing calculated water surface profiles with measured ones, for different river discharges and tides (spring, neap). After calibration, validation has to be done using a different data set.<br />
<br />
<br />
==3D models==<br />
<br />
In 3D models momentum dissipation is represented by Reynolds stresses (time correlations of the turbulent velocity fluctuations <math>u', v', w'</math>) and by boundary conditions at the bed<ref> Chanson, H. (2004) The hydraulics of open channel flow. Elsevier Butterworth Heinemann </ref>. In the case of well mixed estuaries, a simplified turbulence model can be chosen for the Reynolds stresses. In the case of partially mixed or very turbid estuaries, turbulence models must incorporate the effect of density stratification induced by vertical gradients in salinity or suspended sediment<ref>Abraham, G. (1988) Turbulence and mixing in stratified tidal flows. In: Physical Processes in Estuaries (Eds. J. Dronkers and W. van Leussen), Springer, pp. 278-291</ref>. Even weak stratification can strongly suppress turbulence and momentum dissipation <ref> Friedrichs, C. T. and Wright L. D. (1997) Sensitivity of bottom stress and bottom roughness estimates to density stratification, Eckernforde Bay, J. Geophys. Res., 102, 5721–5732</ref>. Modelling of the 3D structure of the salinity or suspended sediment distributions (including the occurrence of fluid mud layers) is thus required in such situations. Calibration of the turbulence model is done by comparing model results with measured velocity and salinity profiles or suspended sediment concentration profiles.<br />
<br />
<br />
==Related articles==<br />
*[[Bedforms and roughness]]<br />
*[[Coastal and marine sediments]]<br />
<br />
<br />
==References==<br />
<br />
<references/><br />
<br />
<br />
==Further reading==<br />
<br />
Tennekes, H. and Lumley, T.L. (1872) A first course in turbulence. M.I.T. Press, Cambridge<br />
<br />
Soulsby, R. (1997) Dynamics of marine sands, Thomas Telford, London<br />
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<br />
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{{author<br />
|AuthorID=49<br />
|AuthorFullName=Jean Berlamont<br />
|AuthorName=U0006958}}<br />
<br />
[[Category:Physical coastal and marine processes]]<br />
[[Category:Estuaries and tidal rivers]]<br />
[[Category:Hydrodynamics]]</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Swash_zone_dynamics&diff=76336Swash zone dynamics2020-01-16T15:25:10Z<p>Dronkers J: </p>
<hr />
<div><br />
==Introduction==<br />
<br />
[[Image: BaldockFig1.jpg|thumb|440px|left|Figure 1. Definition sketch for the nearshore littoral zone (swash zone width exaggerated). After <ref> Elfrink, B. and T. Baldock (2002). Hydrodynamics and sediment transport in the swash zone: a review and perspectives. Coastal Engineering 45: 149-167</ref>.]]<br />
<br />
The swash zone forms the land-ocean boundary at the landward edge of the surf zone, where waves runup the beach face (figures 1, 2). It is perhaps the region of the ocean most actively used by recreational beach users and, being very visible, is the region of the littoral zone most associated with beach erosion and the impacts of climate change. The landward edge of the swash zone is highly variable in terms of geomorphology, and may terminate in dunes, cliffs, marshes, ephemeral estuaries and a wide variety of sand, gravel, rock or coral barriers. This influences the exchange of sediment between the land and ocean, which ultimately forms the coastline.<br />
<br />
In terms of coastal processes and coastal protection, a large part of the littoral sediment transport occurs in the swash zone, both cross-shore and longshore, which influences beach morphology, and beach erosion and beach recovery during and after storms. Wave runup is an important factor in the design of coastal protection and also generates hazards for beach users, and is the dominant process leading to the erosion of coastal dunes. Swash hydrodynamics also influence the ecology of the intertidal zone and groundwater levels in sub-aerial littoral beaches and low lying islands, which is often critical for freshwater water supply on islands and atolls <ref>Nielsen P., 1999. Groundwater dynamics and salinity in coastal barriers. J. Coastal Res., 15: 732-740. </ref>. <br />
<br />
<br />
==Characteristics of the swash zone==<br />
<br />
<br />
{| border="0"<br />
|-<br />
| valign="top"|<br />
[[File:BaldockFig2a.jpg|thumb|445px|left|Figure 2a. Seven Mile Beach, NSW, Australia, a dissipative beach. Photo shows conditions after a swash rundown, with only small bores reaching the swash zone. Photo: Dr Hannah Power, University of Newcastle, NSW, Australia.]]<br />
| valign="top"|<br />
[[File:BaldockFig2b.jpg|thumb|445px|left|Figure 2b. Avoca Beach, NSW, Australia, a reflective beach. Photo shows the inner surf zone and a bore reaching the swash zone in the background and a swash uprush reaching the top of a beach berm in the foreground.]]<br />
|}<br />
<br />
<br />
The hydrodynamic processes in the swash zone are characterised by very different types of fluid flow compared to the open ocean and surf zone, as illustrated in figure 2, where the strongly orbital motion of waves is transformed into flow along the bed (velocity <math>V</math>), usually in thin shallow sheets (thickness <math>d</math>). In terms of fluid mechanics, the key difference is the occurrence of supercritical flow in the swash zone, where the Froude number,<math>V/ \sqrt{gd}</math>, is greater than 1, which has important implications for the nature of the flow. Other important distinctions are that friction becomes more important in controlling aspects of the shallow flow in the swash zone than in the surf zone, and that turbulence and sediment transport in the swash zone is generated locally in the swash zone and advected into the swash zone from the surf zone. A key feature of both the hydrodynamics and sediment dynamics in the swash zone is intermittency, where the extent and degree of inundation of the swash zone varies over different timescales, from orders of seconds and tidal periods to years and decades. This is a challenge for coastal scientists, both in terms of measurement and modelling of the physical processes. For the purposes of this summary, the swash zone will be considered as the region of the beach face exposed to the atmosphere over wind, swell and infragravity wave durations, i.e., seconds to a few minutes.<br />
<br />
The characteristics of the swash zone hydrodynamics and sediment transport are governed by the inner surf zone and the underlying beach, with feedback of course between the morphology and hydrodynamic processes. The beach slope is a controlling parameter <ref>Guza, R. T., Thornton, E. B. and Holman, R. A., 1984. Swash on steep and shallow beaches. Proc. 19th Int. Conf. Coastal Eng., ASCE, 708-723. </ref>. On dissipative beaches, with wide surf zones, most of the wind wave and swell energy is dissipated seaward of the swash zone. Therefore, swash processes are dominated by those due to long, or [[Infragravity waves|infragravity waves]], which are frequently non-breaking standing waves (figure 2a). On intermediate and reflective beaches, short wave energy reaches the beach face in the form of bores or shore-breaks, which collapse at the beach, initiating a runup motion characterised by a thin sheet of water with a rapidly propagating wave tip which is analogous to a [[Dam break flow|dam-break flow]] over a dry bed (figure 2b). This sheet of water is slowed by gravity and friction until the flow reverses and forms another shallow flow seaward, the backwash. On coarse grained sand and [[Gravel Beaches|gravel beaches]] a significant volume of the uprush and some of the backwash may percolate into the beach, reducing the volume of water in the surface backwash flow. These two distinct types of swash zone make modelling hydrodynamic processes difficult, since parametric models rely on similarity of processes, and therefore phase resolving models of the whole surf zone, or at least the inner surf zone, are required if the details of the hydrodynamics are required. Fortunately some processes are modelled very well by parametric models, perhaps more accurately than phase-resolving models, particularly wave runup.<br />
<br />
<br />
==Wave runup and overtopping==<br />
<br />
[[Image: BaldockFig3NEW2.jpg|thumb|500px|left|Figure 3. Typical pattern of bore-driven swash oscillations (vertical component). Data show shoreline elevation versus time at Avoca Beach, NSW. Red and green squares indicate maxima and minima of individual swash events. Data courtesy of Dr Michael Hughes, NSW Office of Environment and Heritage.]]<br />
<br />
Wave runup is perhaps the most important aspect of swash zone flows. While the motion of the water volume as a whole may be considered as runup, conventionally wave runup refers to the landward limit of the swash motion on the beach face, usually defined vertically above the ocean level. The runup and rundown of the shoreline is referred to as the swash excursion or oscillation. A typical plot of the shoreline motion is shown in figure 3.<br />
<br />
Remarkably, the maximum runup is still most reliably described by a simple empirical parametric formula, which is perhaps one of the oldest regularly in use, proposed by Hunt (1959). Despite numerous variations, the underlying scaling still holds over a very large range of wave conditions, both in the laboratory and field.<br />
The scaling for runup proposed by Hunt <ref>Hunt, I.A., 1959. Design of sea-walls and breakwaters. Transactions of the American Society of Civil Engineers, 126: 542-570. </ref> is:<br />
<br />
<math>R_{max}=\xi H_0 = \tan \beta \sqrt{H_0 L_0} , \qquad (1)</math><br />
<br />
where <math>\xi</math> is the surf similarity parameter, or Iribarren number (<math>\xi =\tan\beta / \sqrt{H_0/L_0})</math> and <math>H_0, L_0</math> and <math>\beta</math> are offshore wave height, wave length and the swash zone beach face slope, respectively. This is strictly only applicable for monochromatic waves and the maximum runup. However, the same formulation has been widely used to describe random wave runup, using appropriate [[Statistical description of wave parameters|statistical parameters to describe the wave conditions]]. This parameter is usually the runup elevation exceeded by 2% of the waves, <math>R_{2\%}</math>. The most widely used derivative of Hunt's formula is perhaps due to Stockdon et al. <ref name=S> Stockdon, H. F., Holman, R. A., Howd, P. A. & Sallenger JR, A. H. 2006. Empirical parameterization of setup, swash, and runup. Coastal Engineering, 53, 573-588.</ref>, which also allows for a contribution from infragravity waves:<br />
<br />
<math> R_{2\%} = 1.1 \; \left( 0.5 \sqrt{H_s L_p \; (0.563 \beta^2 + 0.004)} +0.35 \; \beta \sqrt{H_s L_p} \right) , \qquad \xi_p \ge 0.3 , \qquad (2)</math><br />
<br />
<math> R_{2\%}= 0.43 \; \beta \sqrt{H_s L_p} , \qquad \xi_p < 0.3 , \qquad (3)</math><br />
<br />
where the term <math>0.35 \; \beta \sqrt{H_s L_p}</math> represents the setup, <math>H_s</math> is the deep water significant wave height, and <math>L_p</math> is the wavelength corresponding to the deep water peak wave period, <math>T_p</math>. Atkinson et al. <ref>Atkinson, A.L., Power, H.E., Moura, T., Hammond, T., Callaghan, D.P. and Baldock, T.E., 2017. Assessment of runup predictions by empirical models on non-truncated beaches on the south-east Australian coast. Coastal Engineering, 119: 15-31. </ref> compared a number of recent runup formulations to measurements from a range of beaches and concluded that the models generally predict runup with errors of order <math>\pm 25 \%</math>.<br />
<br />
[[Image: BaldockFig4.jpg|thumb|500px|left|Figure 4. Swash energy spectra from (a) reflective, (b) intermediate, and (c) dissipative beach-states. The grey lines show individual spectra, the coloured lines show the average spectrum for the beach-state, the black line represents an <math>f^{-4}</math> energy roll-off and the vertical dashed line demarcates the short-wave and long-wave frequency bands. From Hughes et al. <ref>Hughes, M. G., T. Aagaard, T. E. Baldock and H. E. Power, 2014. Spectral signatures for swash on reflective, intermediate and dissipative beaches. Marine Geology 355: 88-97. </ref>, with permission.]]<br />
<br />
Swash-swash interactions occur through the overtaking of a swash uprush by the following bore or during the collision of the backwash flow with the next uprush. The magnitude, or vertical excursion, of the swash oscillations, from rundown position to runup, is strongly influenced by interaction between wave uprush and backwash, with the period of the incident waves also controlling the period of the swash oscillations at swell and wind wave frequencies <ref>Holman, R. A. 1986. Extreme value statistics for wave runup on a natural beach. Coastal Engineering, 9: 527-544. </ref>. Hence, given a finite time for the uprush and backwash to occur, there is a finite magnitude for a swash oscillation at a given frequency on a given beach slope if the motion is solely controlled by gravity. This leads to swash saturation, where an increase in incident wave height does not increase the magnitude of the swash oscillations. This can be parameterised for individual events, or through a spectral representation.<br />
<br />
For non-breaking monochromatic waves, this limit is given by Miché <ref>Miché, R., 1951. Le pouvoir réfléchissant des ouvrages maritimes exposés à l'action de la houle. Ann. Ponts et Chaussees, 121: 285-319. </ref>:<br />
<br />
<math>\varepsilon_s=\Large \frac{a_s \omega^2}{g \beta^2} \normalsize = 1 , \qquad (4)</math><br />
<br />
where <math>a_s</math> is the vertical amplitude of the shoreline motion, <math>\omega</math> is the angular wave frequency (<math>=2 \pi f</math> - where <math>f</math> is the wave frequency), <math>g</math> the gravitational acceleration and <math>\beta</math> the beach slope. This assumes a saturated surf zone and, based on the limiting amplitude for monochromatic unbroken standing waves, <math>\varepsilon \approx 1</math>. For swash initiated by breaking wave bores, Baldock and Holmes <ref name=B>Baldock T. E. and Holmes P., 1999. Simulation and prediction of swash oscillations on a steep beach. Coastal Engineering, 36: 219-242. </ref> derived a theoretical value <math>\varepsilon \approx 2.5</math>, where saturation is controlled by swash-swash interaction as opposed to surf zone saturation. Spectra of the shoreline oscillations also indicate saturation at higher frequencies, with a typical roll-off in the energy density that is proportional to <math>f^{-4}</math>, which is also evident from equation 4. Huntley et al. <ref>Huntley, D. A., R. T. Guza and A. J. Bowen, 1977. Universal form for shoreline runup spectra. Journal of Geophysical Research-Oceans and Atmospheres 82: 2577-2581. </ref> proposed a uniform spectral form for saturated swash spectra, but variations occur due to different surf zone conditions (figure 4).<br />
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[[Image: BaldockFig5.jpg|thumb|300px|right|Figure 5. Washover fan deposited on Ocracoke Island, North Carolina, during Hurricane Isabel, September 2003. Source: Adapted from Donnelly, Kraus, and Larson (2006) <ref>Donnelly, C., N. Kraus and M. Larson, 2006. State of knowledge on measurement and modeling of coastal overwash. Journal of Coastal Research 22: 965-991. </ref>. Reproduced with permission of the Coastal Education and Research Foundation, Inc.]]<br />
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When the runup exceeds the elevation of the crest of a structure, beach berm or dunes, wave overtopping or wave overwash occurs. This process is very important in building beach berms higher, in association with the spring-neap tidal cycle, but also leads to coastal flooding and inundation of the backshore region. The geomorphology of barrier islands and gravel barriers is strongly dependent on swash overtopping, and breaching of these systems by landward transport of sediment during the overtopping can lead to rapid and potentially [[Dune erosion|catastrophic failure of protective coastal barriers]] (figure 5). The response of coastlines to sea level rise is also be influenced by swash overtopping and sediment overwash, which increases recession in comparison to the classical [[Bruun rule for shoreface adaptation to sea-level rise|Bruun Rule]] <ref>Rosati, J. D., R. G. Dean and T. L. Walton, 2013. The modified Bruun Rule extended for landward transport. Marine Geology 340: 71-81. </ref>. A combination of parametric modelling and numerical techniques is required to model these scenario <ref>Roelvink, D., Reniers, A., Van Dongeren, A.P., de Vries, J.V.T., McCall, R. and Lescinski, J., 2009. Modelling storm impacts on beaches, dunes and barrier islands. Coastal engineering, 56: 1133-1152. </ref><br />
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==Swash zone hydrodynamics==<br />
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[[Image: BaldockFig6.jpg|thumb|500px|left|Figure 6. Forward (solid) and backward (dashed) characteristic curves (a), and contours of flow velocity (b), surface elevation (c) and depth (d) for swash initiated by a near uniform bore in the non-dimensional coordinates of Peregrine and Williams <ref name=P></ref>. Dotted lines in panel (a) show locus of u=c (critical flow) for uprush and backwash. From <ref name=GB></ref>, with permission.]]<br />
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Swash zone flows have several features that differ from those in the surf zone, but this is dependent on the dominant wave conditions in the inner surf zone as noted above. Many key characteristics again depend on the Iribarren number <ref> Roos, A. and Battjes, J.A., 1977. Characteristics of flow in runup of periodic waves. Proc. 15th International Conference on Coastal Engineering, ASCE, pp. 781-795</ref>. For infragravity standing long waves, the variation in flow depth and flow velocity at a point is relatively symmetrical during uprush and backwash. Short wave bores generate more asymmetrical flows, with the maximum velocity occurring at the start of inundation, with a rapid rise to the maximum depth, with an almost linear deceleration to flow reversal, and a correspondingly similar uniform acceleration in the backwash, at least until the flow becomes very shallow, when friction retards the flow significantly. A key aspect of these flows is diverging flow, which means the swash lens thins rapidly.<br />
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Runup and backwash velocities in the field reach 2-5 m/s, which are generally larger than those in the surf zone. The runup durations are typically shorter than the backwash duration, and the backwash depths are shallower than during the uprush, and therefore the velocity moments tend to be skewed offshore, which has important implications for the sediment dynamics <ref>Raubenheimer, B., R. T. Guza, S. Elgar and N. Kobayashi, 1995. Swash on a gently sloping beach. Journal of Geophysical Research-Oceans 100(C5): 8751-8760. </ref>. The asymmetry is however affected by the mass and momentum advected into the swash zone, which depends on the flow in the inner surf zone. Self-similar solutions for different boundary conditions are presented by Guard and Baldock <ref name=GB>Guard, P. A. and T. E. Baldock, 2007. The influence of seaward boundary conditions on swash zone hydrodynamics. Coastal Engineering 54: 321-331. </ref>, following the work of Peregrine and Williams <ref name=P>Peregrine, D. H. and S. M. Williams, 2001. Swash overtopping a truncated plane beach. Journal of Fluid Mechanics 440: 391-399. </ref>, figure 6. These indicate the fundamental nature of the hydrodynamics, which comprise of a near parabolic motion of the shoreline (due to gravity being the dominant process) and a saw-tooth shaped variation in velocity with time, which decreases at a near linear rate from the peak velocity, which occurs as the shoreline passes a given location. The water surface slope dips seaward for nearly the whole swash cycle, i.e. the total fluid acceleration is offshore throughout the swash cycle.<br />
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This results in a key difference between the surf zone and swash zone bed boundary conditions, namely that there is generally little phase lag between velocity and the bed shear stress in the swash zone, i.e. maxima in bed shear stress occur close to the instants of maxima in velocity. Close to the time of flow reversal, the flow near the bed does however reverse prior to the flow higher in the water column, due to the adverse pressure gradient during the uprush <ref>Kikkert, G. A., T. O'Donoghue, D. Pokrajac and N. Dodd, 2012. Experimental study of bore-driven swash hydrodynamics on impermeable rough slopes. Coastal Engineering 60: 149-166. </ref>. The boundary layer is thinnest at the seaward edge of the swash zone during uprush, and grows following the flow up the beach. The boundary layer largely vanishes at flow reversal, and again grows from the bed as the flow recedes. Accounting for such processes in sediment transport models remains to be tackled.<br />
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[[Image: BaldockFig7NEW.jpg|thumb|400px|right|Figure 7. Contours of surface elevation with two different resistance coefficients, R=0 (blue lines) and R=0.01 (red dashed lines) in the non-dimensional coordinates of Peregrine and Williams <ref name=P></ref>. From Deng et al. <ref>Deng, X., H. Liu, Z. Jiang and T. E. Baldock, 2016. Swash flow properties with bottom resistance based on the method of characteristics. Coastal Engineering 114: 25-34</ref>, with permission.]]<br />
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There are several sources of turbulence in the swash zone. In the runup, turbulence is advected from the inner surf zone, which combines with further generation of turbulence at the bed. The boundary layer is evolving, generally increasing in thickness and may become depth limited. During the backwash turbulence generation occurs mainly at the bed, with swash-swash interactions generating further turbulence as the next wave arrives. Overall, the high turbulence near the bed leads to high bed shear stresses and the potential for high concentrations of suspended sediment transport <ref>Puleo, J. A., R. A. Beach, R. A. Holman and J. S. Allen, 2000. Swash zone sediment suspension and transport and the importance of bore-generated turbulence. Journal of Geophysical Research-Oceans 105(C7): 17021-17044. </ref>.<br />
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Friction plays a large role in controlling the shoreline motion, with friction factors based on conventional fluid mechanics principles typically in the range <math>0.02<f<0.1</math>. Friction effects are strongest when the flow is shallowest, at the swash tip, reducing runup excursions, and late in the backwash, so the shoreline recedes more slowly. Simple models, comprising of a ballistic motion plus friction, describe the shoreline motion reasonably well, although details are missing <ref>Hughes M. G., 1995. Friction factors for wave uprush. J. Coastal Res., 13: 1089-1098</ref><ref name=PH>Puleo, J. A. and K. T. Holland, 2001. Estimating swash zone friction coefficients on a sandy beach. Coastal Engineering 43: 25-40</ref>. Inclusion of friction effects in the internal flow requires numerical modelling at present, or the use of integral models which can avoid the uncertainty in the treatment of friction at the shoreline <ref>Archetti, R. and M. Brocchini, 2002. An integral swash zone model with friction: an experimental and numerical investigation. Coastal Engineering 45: 89-110. </ref>. However, recent results suggest that the effects of friction on the internal flow are small compared to the effects at the swash tip. For example, figure 7 shows a method of characteristics solution for the swash flow with and without friction. The numerical results indicate that the two solutions are similar when water is present, which is interesting given the significant effect of friction on the location of the shoreline. The reason is the supercritical nature of the flow, which is a particular feature of the swash zone. This means that the large change in the shoreline position due to friction does not significantly affect the flow seaward of the shoreline until the flow becomes subcritical, which does not occur until late in the uprush. Similarly, the supercritical nature of the backwash flow means that the changes to the shoreline position further landward cannot significantly affect flow further seaward. Thus, the supercritical nature of the swash flow means that the significant changes in shoreline position do not significantly affect the flow in the interior of the swash lens.<br />
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==Sediment transport mechanics==<br />
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[[Image: BaldockFig8.jpg|thumb|400px|left|Figure 8. A turbulent bore containing entrained suspended sediment just prior to reaching the swash zone. The sediment is then advected into the swash zone during the runup. The end of a supercritical backwash flow is visible in the right of the image. The posts are 1m apart and the orange stringlines are horizontal. Source: Adapted from Hughes, Aagaard, and Baldock (2007) <ref name=H></ref>. Reproduced with permission of the Coastal Education and Research Foundation, Inc.]]<br />
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Cross-shore sediment transport in the swash zone generally occurs as a combination of bed load under sheet flow conditions, with a flat bed, plus an additional component of suspended load, generated locally and advected into the swash zone by surf zone bores. For the bed load, the Meyer-Peter and Muller <ref> Meyer-Peter, E. and Müller, R., 1948. Formulas for bed-load transport. Proc. IAHR, Stockholm </ref> formulation, or derivatives, generally perform well with calibration, i.e. determining the transport coefficient and friction factor remain problematic. In these models, the transport is typically a function of the velocity cubed. The relative balance between bed load, which is generated locally, and suspended load depends on the sediment grain size, and also on the quantity of sediment advected into the swash zone from the inner surf zone (figure 8). This can be considerable, and affects the distribution of suspended load across the swash zone. While the basic sediment transport equations still apply, model-data comparisons are lacking, particularly close to the bed where suspended sediment concentrations are largest.<br />
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[[Image: BaldockFig9.jpg|thumb|350px|right|Figure 9. Measured normalized suspended sediment concentration <math>c </math> indicated by colours mapped onto the normalised <math>x_* - t_*</math> plane representing the swash excursion and duration. Colour bar indicates normalised concentration from high (hot) to low (cold). Source: Adapted from Hughes, Aagaard, and Baldock (2007) <ref name=H></ref>. Reproduced with permission of the Coastal Education and Research Foundation, Inc.]]<br />
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In simple <math>u^3</math> type sediment transport models the asymmetry of the flow tends to export sediment from the swash zone. In reality, this is balanced by the suspended sediment imported and advected into the swash zone from the inner surf <ref name=H>Hughes, M. G., T. Aagaard and T. E. Baldock, 2007. Suspended sediment in the swash zone: Heuristic analysis of spatial and temporal variations in concentration. Journal of Coastal Research 23: 1345-1354. </ref>, the distribution of which is illustrated in figure 9. Measurement of suspended sediment in the backwash remains a challenge, and is difficult to separate from bed-load. The quantity of suspended load entering the swash zone affects the net deposition pattern, and hence zones of erosion or accretion, as illustrated by Pritchard and Hogg <ref>Pritchard, D. and A. J. Hogg, 2005. On the transport of suspended sediment by a swash event on a plane beach. Coastal Engineering 52: 1-23</ref>. Data is still lacking in the field to reliably quantify this process, which is complicated by sediment suspended by swash-swash interactions and the influence of turbulence in the inner surf zone, which is significant <ref>Butt, T., P. Russell, J. Puleo, J. Miles and G. Masselink, 2004. The influence of bore turbulence on sediment transport in the swash and inner surf zones. Continental Shelf Research 24(7-8): 757-771. </ref>. The infiltration and exfiltration of water into the beach during swash flows is an important contributor to groundwater processes, particularly on coarse grain beaches, and also influences sediment transport <ref>Turner, I.L. and G. Masselink, 1998. Swash infiltration-exfiltration and sediment transport. Journal of Geophysical Research, 103(C13): 30,813-30,824</ref>.<br />
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The mechanics of longshore sediment transport in the swash zone are well-understood in principle, but data and modelling is limited, despite the clear presence of a significant contribution to the total [[Littoral drift and shoreline modelling|longshore transport in the littoral zone]]. In the swash zone the flow direction during both runup and rundown has a longshore component under oblique waves (the usual case). The boundary between the surf and swash zone is also an active region of longshore transport, particularly on steep cobble or coral beaches, where sediment may also move offshore into the inner surf zone, then alongshore, and then back onshore as the wave conditions or tide change <ref>Kench, P. S., E. Beetham, C. Bosserelle, J. Kruger, S. M. L. Pohler, G. Coco and E. J. Ryan, 2017. Nearshore hydrodynamics, beach face cobble transport and morphodynamics on a Pacific atoll motu. Marine Geology 389: 17-31. </ref>. While the relative importance of longshore transport in the swash zone compared to the surf zone is greater during milder wave conditions than during storms, longshore sediment transport in the swash zone may account for up to 50% of the total longshore transport <ref>Kamphuis J. W., 1991. Alongshore sediment transport rate distribution. Coastal Sediments '91 Conference, ASCE, 170-183. </ref>. Longshore transport in the swash zone is also relatively more important on steep beaches and where small oblique waves break frequently at the shoreline, e.g., in estuary mouths and landward of lagoons behind fringing and barrier reefs.<br />
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==Morphodynamics==<br />
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The evolution of the beach face in the swash zone is controlled by the sediment fluxes across the boundaries, both longshore and cross-shore. Thus, the morphology is influenced by the presence of dunes, cliffs and hard structures at the landward extent of the beach, by conditions in the inner surf one, notably bars, rip cells, beach steps, and by lateral boundaries such as groynes, breakwaters and estuary mouths. While the general processes are again well understood, and similar to those applied for littoral transport in the surf zone, the details of [[Dune erosion|dune erosion]], barrier degradation and progradation and the short and long term balance of sediment deposition and erosion remain a challenge <ref> Masselink, G. and J. A. Puleo (2006). Swash-zone morphodynamics. Continental Shelf Research 26(5): 661-680</ref>. For example, rates of deposition and erosion vary significantly on wave-by-wave time scales, wave group time-scales, and tidal time-scales, plus seasonal and annual changes due to variations in wave and wind climate. Further, while the active swash zone is usually relatively plane (excluding dunes), feedback between morphology and hydrodynamics does lead to more complex morphology such as [[Beach Cusps]]. Varying tides also lead to the formation of beach ridges and berms at different elevations, which complicate the overall topography. Dunes act as significant sources and sinks of sediment that control swash zone morphodynamics and that of the whole beach, and are essential in developing the sediment budget for the whole beach. A further aspect is the influence of vegetation, which can provide important [[Dune stabilisation|stabilising mechanisms for dunes]]. The upper beach and swash zone is where the impacts of sea level rise will be most visible, with loss of the upper beach if the coastline cannot recede landward.<br />
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==Measurement techniques==<br />
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[[Image: BaldockFig10.jpg|thumb|500px|left|Figure 10. A LIDAR system mounted above the swash zone, together with ultrasonic distance point sensors. Photo: Dr Chris Blenkinsopp, University of Bath, UK.]]<br />
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Research on swash zone processes is both assisted and hindered by the nature of the swash. The beach face is generally accessible for deployment of instruments, particularly with the aid of large tides, it is close to the shore and associated infrastructure, and much wave energy has been dissipated in the surf zone. However, flows are very shallow and also intermittent, making measurements over the depth difficult and time-averaging complex. In terms of in-situ instruments, the shoreline motion can be measured by runup wires or point instruments such as pressure sensors or ultrasonic sensors, flow velocity with electromagnetic or acoustic instruments, and morphology changes with standard survey techniques or ultrasonic sensors. To tackle larger scales and to avoid in-situ measurements and to sample over longer time-scales, [[Argus applications|remote sensing by video]] has adopted techniques first developed for the surf zone by Aagaard and Holm <ref>Aagaard, T. and J. Holm, 1989. Digitization of wave runup using video records. Journal of Coastal Research 5: 547-551. </ref> to determine friction factors <ref name=PH></ref>, runup <ref name=S></ref> and internal kinematics <ref>Power, H. E., R. A. Holman and T. E. Baldock, 2011. Swash zone boundary conditions derived from optical remote sensing of swash zone flow patterns. Journal of Geophysical Research, Oceans 116, C06007, doi:10.1029/2010JC006724</ref>. Shore-mounted LIDAR is becoming a promising tool for high resolution and long term monitoring <ref>Blenkinsopp, C. E., M. A. Mole, I. L. Turner and W. L. Peirson, 2010. Measurements of the time-varying free-surface profile across the swash zone obtained using an industrial LIDAR. Coastal Engineering 57(11-12): 1059-1065. </ref>, figure 10. However, both these techniques suffer from loss of resolution in the thinning backwash, and do not provide flow velocity with any degree of reliability. Sediment transport measurements using sediment traps <ref>Horn, D. P. and T. Mason, 1994. Swash zone sediment transport modes. Marine Geology 120(3-4): 309-325. </ref><ref> Masselink, G. and M. Hughes (1998). Field investigation of sediment transport in the swash zone. Continental Shelf Research 18(10): 1179-1199</ref> still provide the most reliable measure of total load transport rates in the field, supplemented by sediment transport rates derived from morphological measurements through sediment continuity, which can be particularly useful during overwash events. Both techniques require predominantly cross-shore transport.<br />
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==Related articles==<br />
: [[Beach Cusps]]<br />
: [[Infragravity waves]]<br />
: [[Gravel Beaches]]<br />
: [[Shallow-water wave theory]]<br />
: [[Dam break flow]]<br />
: [[Sand transport]]<br />
: [[Rhythmic shoreline features]]<br />
: [[Bruun rule for shoreface adaptation to sea-level rise]]<br />
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==References==<br />
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{{author<br />
|AuthorID=34603<br />
|AuthorFullName=Tom Baldock<br />
|AuthorName= Tom Baldock}}<br />
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[[Category:Physical coastal and marine processes]]<br />
[[Category:Beaches]]<br />
[[Category:Sediment]]<br />
[[Category:Hydrodynamics]]<br />
[[Category:Morphodynamics]]</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Coastal_hydrodynamic_and_morphodynamic_processes_and_engineering&diff=76335Coastal hydrodynamic and morphodynamic processes and engineering2020-01-15T20:50:32Z<p>Dronkers J: </p>
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<div><br />
==Introduction==<br />
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This article presents an overview of the Coastal Wiki content (July 2017) on coastal hydrodynamic and morphodynamic processes, long term geomorphological change, climate impacts and coastal engineering (articles in blue). This content was initiated by the ENCORA themes 5 and 8. <br />
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The article also indicates missing topics (articles in red). <br />
Please help us fill these gaps by expanding and claiming these missing topics. <br />
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For some gaps alternative websites are indicated, in particular:<br />
* pages of Wikipedia<br />
* pages of the Australian coastal website https://ozcoasts.org.au/<br />
* pages in English of the Dutch Deltaproof website http://deltaproof.stowa.nl/Publicaties/deltafact.aspx?pId=1739<br />
* pages on the website of Leo van Rijn https://www.leovanrijn-sediment.com/<br />
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See also: [[Definitions of coastal terms]].<br />
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== Coastal hydrodynamics ==<br />
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'''Coastal Wiki articles'''<br />
* [[Hydrodynamic modelling]] <br />
* [[Modelling coastal hydrodynamics]] <br />
* [[How to apply models]] <br />
* [[Reduction of uncertainties through Data Model Integration (DMI)]]<br />
* [[Using model simulations to support monitoring - Methods&Techniques]]<br />
* [[Using model simulations to support monitoring - Implementation & Results]]<br />
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'''Coastal Wiki gap'''<br />
* [[Hydrodynamic processes and equations]] - introduction to the mathematical formulation of major physical processes that should be addressed in models for different types of coastal systems (sediment transport formulas are addressed in other articles)<br />
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===Waves===<br />
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'''Coastal Wiki articles'''<br />
* [[Shallow-water wave theory]] <br />
* [[Waves and currents by X-band radar]] - wave measurement technique<br />
* [[Using satellite data for global wave forecasts]]<br />
* [[Infragravity waves]]<br />
* [[Tsunami]] <br />
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'''Incomplete articles'''<br />
* [[Waves]] – more comprehensive introduction to wave phenomena and wave types: progressive, standing, surface, internal, gravity, capillary, wind wave, swell, tide, planetary or Rossby waves, tsunami, ship waves. <br />
* [[Wave transformation]] , see [[Shallow-water wave theory]] <br />
* [[Edge waves]] definition should be expanded: periods incident waves, reflection, dissipation, propagation, coastally trapped waves<br />
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'''Coastal Wiki gaps'''<br />
* [[Wind wave generation]] – introduction to underlying processes, fetch, saturated wave field, wave-wave interaction, wave spectrum <br />
* [[Wave transformation in the nearshore]] – extension of [[Shallow-water wave theory]] with more detailed treatment of propagation of random waves into shallow water, wave breaking and dissipation mechanisms, breaking criteria, roller energy, wave asymmetry and skewness, cnoidal waves, solitary waves, observations, empirical formulas, models<br />
* [[Surf zone dynamics]] – impact of [[Wave transformation in the nearshore]] on nearshore morphology<br />
* [[Wave-current interaction]]<br />
* [[Wave impact]] – stability of structures under wave attack <br />
* [[Ship waves]] - wash or wake, Kelvin wave pattern, supercritical wash<br />
* [[Wave modelling]] - operational, coastal, computational fluid dynamics, smoothed particle hydrodynamics<br />
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'''External references'''<br />
* [https://en.wikipedia.org/wiki/Category:Water_waves Water waves] <br />
* [https://en.wikipedia.org/wiki/Airy_wave_theory Airy wave theory]<br />
* [https://en.wikipedia.org/wiki/Cnoidal_wave Cnoidal wave]<br />
* [https://en.wikipedia.org/wiki/Wind_wave Wind wave]<br />
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===Tides===<br />
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'''Coastal Wiki articles'''<br />
* [[Ocean and shelf tides]]<br />
* [[Tidal motion in shelf seas]] <br />
* [[Tidal asymmetry and tidal basin morphodynamics]]<br />
* [[Tidal bore dynamics]]<br />
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'''Incomplete articles'''<br />
* [[Storm surge]] definition needs expansion: storm surge prediction, storm surge modelling, storm surge impact <br />
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'''External references'''<br />
* [https://en.wikipedia.org/wiki/Theory_of_tides Theory of tides]<br />
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===Currents===<br />
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'''Coastal Wiki articles'''<br />
* [[Currents]] introduction to currents in the Open Sea (tidal, wind-generated, storm surge), current in the nearshore zone (shore-parallel, shore-normal, undertow, rip currents, cross-currents), two-dimensional currents in the nearshore zone <br />
* [[Waves and currents by X-band radar]] - measurement method of currents <br />
* [[Currents and turbulence by acoustic methods]] - measurement method of currents <br />
* [[Use of ground based radar in hydrography]] - measurement method of currents <br />
* [[Measuring current fields in the German Bight by radar techniques]] <br />
* [[Application of radar hydrography in the German Wadden Sea]]<br />
* [[Coriolis acceleration]]<br />
* [[Bedforms and roughness]]<br />
* [[Bed roughness and friction factors in estuaries]] <br />
* [[Dam break flow]]<br />
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'''Incomplete articles'''<br />
* [[Rip currents]] – extension of [[Rhythmic shoreline features]] with a more detailed treatment of characteristics of rip-cells, their importance, occurrence, hydrodynamics, morphodynamic feedbacks, influence of tides, storms, modelling, practical formulas, implications for coastal management <br />
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'''Coastal Wiki gaps'''<br />
* [[Wind driven currents]] – sea surface entrainment, turbulence, Ekman theory<br />
* [[Density-driven currents]] – buoyancy, stratification, turbulence damping, entrainment, modelling<br />
* [[Turbulence]] – generation, coherent flow structures, dissipation, Kolmogorov theory, spectrum, shear stress, diffusion, mixing length<br />
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==Transport and mixing processes==<br />
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'''Coastal Wiki articles'''<br />
* [[Seawater intrusion and mixing in estuaries]]<br />
* [[Estuarine circulation]]<br />
* [[Salt wedge estuaries]]<br />
* [[Dynamics and structure of the water and matter ex-change between the Wadden Sea and the German Bight]]<br />
* [[Transport and dispersion of pollutants, nutrients, tracers in mixed nearshore water]]<br />
* [[Shelf sea exchange with the ocean]]<br />
* [[Suspended particulate matter distribution in the North Sea]]<br />
* [[Index of vulnerability of littorals to oil pollution]] <br />
* [[Oil spill monitoring]]<br />
* [[Water quality services GMES - MarCoast in Germany]]<br />
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'''Incomplete articles'''<br />
* [[Stratification]] – needs expansion: stability criteria, internal waves, Kelvin-Helmholz instability, turbulence damping, internal friction, mixing<br />
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'''Coastal Wiki gaps'''<br />
* [[Transport and mixing processes in shelf seas]] - introduction to concepts and processes, field studies, modelling, ecosystem implications <br />
* [[River plume dynamics]] - introduction to major physical processes, observation methods, field examples and practical simulation models<br />
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'''External references'''<br />
* [http://deltaproof.stowa.nl/pdf/Salt_intrusion?rId=84 Reduction of saline intrusion]<br />
* [https://en.wikipedia.org/wiki/Oil_spill Oil spill]<br />
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==Flood risk==<br />
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'''Coastal Wiki articles'''<br />
* [[Chances and risks]]<br />
* [[Extreme storms]]<br />
* [[Decision Support Systems for coastal risk assessment and management]] <br />
* [[Risk and coastal zone policy: example from the Netherlands]] <br />
* [[Flood risk analysis study at the German Bight Coast]]<br />
* [[Shoreline management]]<br />
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'''Coastal Wiki gaps'''<br />
* [[Extreme event analysis]] - Gumbel, Weibull distributions, exceedance probability, dependence and joint probability, return period<br />
* [[Flood risk]] general article<br />
* [[Risk management strategies]] general article <br />
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== Coastal sediments and sediment transport==<br />
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'''Coastal Wiki articles'''<br />
* [[Coastal and marine sediments]]<br />
* [[Manual Sediment Transport Measurements in Rivers, Estuaries and Coastal Seas]] series of articles on sediment transport measurement, with many subtopics <br />
* [[Sediment deposition and erosion processes]] <br />
* [[Dynamics of mud transport]]<br />
* [[Sand transport]]<br />
* [[Sediment transport formulas for the coastal environment]]<br />
* [[Coastal Hydrodynamics And Transport Processes]] - introduction to sediment transport in general, onshore and offshore transport and equilibrium coastal profile, transport of non-cohesive sediments <br />
* [[Wave ripples]]<br />
* [[Wave ripple formation]]<br />
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<br />
'''Coastal Wiki gaps''' <br />
* [[Sediment budget coastal systems]] <br />
* [[Boundary layer processes and sediment transport]] - introduction to the boundary layer concept (waves, current, waves+current), turbulence, temporal-spatial scales, bed-flow interaction, velocity and acceleration skewness, flat/rippled/sloping beds, sediment transport processes, onshore-offshore asymmetry, observation, modelling, practical formulas<br />
* [[Current ripples and dunes]] – formation processes, theoretical background, modelling<br />
* [[Cross-shore sediment transport]] - shoaling zone, breaker zone, swash zone<br />
* [[Aeolian transport]] – from beach to dunes, influence of grainsize, fetch, tides, moisture, vegetation, dune formation, modelling<br />
* [[Estuarine sedimentation and turbidity maximum]] - introduction to characteristics of turbidity maxima, underlying processes (tidal asymmetry, estuarine circulation), impact on sedimentation and water quality, conditions of occurrence, relation with dredging and reclamation in estuaries, observations, modelling<br />
<br />
<br />
==Coastal morphology==<br />
<br />
===Wave-dominated coasts===<br />
<br />
'''Coastal Wiki articles'''<br />
* [[Classification of coastlines]] deals with nearly straight coastlines (with overview of coastal characteristics), special coastal planforms (delta coastlines, sand spits, barrier islands, mechanisms and conditions for barrier island development), barrier formation; effect of development<br />
* [[Characteristics of sedimentary shores]] - introduction to different coastal types<br />
* [[Active coastal zone]]<br />
* [[Closure depth]]<br />
* [[Shoreface profile]]<br />
* [[Swash zone dynamics]] <br />
* [[Gravel Beaches]]<br />
* [[Littoral drift and shoreline modelling]] needs expansion and update of longshore sediment transport with recent formulas<br />
<br />
<br />
'''Incomplete articles'''<br />
* [[Rocky shore morphology]] – needs expansion to cliff morphology, sediment input, shore platforms, stacks, headlands, etc.<br />
* [[Beach berm]] – expand definition and add section on berm formation <br />
<br />
<br />
'''Coastal Wiki gaps''' <br />
* [[Typology of coastlines]] – introduction to different coastline classification schemes, accretional, erosional coasts, beaches, estuaries, inlets, deltas, cliffs, mudflats, dunes, stacks, headlands, blowholes<br />
* [[Embayed beaches]] - morphodynamics and equilibrium planform of beaches that are semi-enclosed by headlands or groynes. <br />
* [[Wave-dominated coast]] general introduction: barriers, beaches, breaker bars, intertidal bars and runnels <br />
* [[Macrotidal coasts]] - introduction to: characteristics of macrotidal coasts (compared to micro- or mesotidal coasts), variability, major involved hydrodynamic and morphodynamic processes, resilience, response to sea-level rise<br />
* [[Mud coasts]] (or [[Fluvial-dominated coasts]] ) - introduction to the particular characteristics of mud coasts (compared to sand coasts) and the processes responsible for their formation, evolution and maintenance, threats and response to sea-level rise<br />
* [[Typology of mangrove coasts]] – morphological-ecological interaction<br />
* [[Coastal barrier formation]] - introduction to characteristics of coastal barriers, their importance, processes responsible for their formation, evolution and maintenance, threats to existing coastal barriers (human interventions and sea-level rise), good management practices <br />
* [[Breaker bar dynamics]] – development, evolution and decay of breaker bars in the surf zone, underlying morphodynamic processes and modelling <br />
* [[Beach-dune interaction]] - introduction to major processes of coastal dune formation and erosion, and practical modelling concepts<br />
* [[Reef systems]]<br />
<br />
<br />
'''External references'''<br />
* [https://ozcoasts.org.au/conceptual-diagrams/science-models/beaches/ OzCoast Beaches]<br />
<br />
===Deltas, estuaries and lagoons===<br />
<br />
'''Coastal Wiki articles'''<br />
* [[Morphology of estuaries]] - classification of estuaries, tide-dominated, river-dominated, wave-dominated estuaries, examples <br />
* [[Wave-dominated river deltas]] <br />
* [[Estuarine morphological modelling]] <br />
* [[Physical processes and morphology of synchronous estuaries]]<br />
* [[Siltation in harbors and fairways]]<br />
* [[Salt marshes]] <br />
* [[Dynamics, threats and management of salt marshes]] <br />
* [[Salt marshes in Europe and temporal variability]]<br />
* [[Tidal asymmetry and tidal basin morphodynamics]]<br />
<br />
'''Incomplete articles'''<br />
* [[Estuaries and tidal rivers]] – introduction to different types of estuaries<br />
* [[Mudflat]] – needs expansion of existing definition, mudflat morphology and morphodynamics (interaction morphology-tide-waves-biology), link to saltmarsh morphology<br />
* [[Salt marsh morphodynamics]] – typical salt marsh morphologies, introduction to underlying physical feedback processes (interaction waves, tide with morphology), biogeomorphodynamics <br />
* [[Fjords]] – definition needs to be expanded: formation process, hydrodynamics <br />
* [[Coastal squeeze]] – article must be revised and expanded: introduction to the concept of coastal squeeze, influential factors, how does it happen, consequences, examples, how to avoid, how to mitigate, lessons from practice<br />
* [[Characteristics of muddy coasts ]] - needs revision and expansion to include wave influence and interactions ecology-hydrodynamics-morphology. <br />
<br />
<br />
'''Coastal Wiki gaps''' <br />
* [[Rias]] – definition, impact of geological constraints on hydrodynamics and morphodynamics <br />
* [[Tidal lagoons]] – evolution, morphodynamics<br />
* [[Tide-dominated river deltas]] - introduction to characteristics of tidal deltas with high liquid and solid river discharge, major processes for their formation, evolution and maintenance, resilience and threats, response to sea-level rise<br />
* [[Ebb-tidal deltas]] – tide- and wave-driven morphodynamics, interaction with tidal basin morphodynamics<br />
* [[Estuarine morphodynamics]] – morphodynamic feedback, equilibrium planform, equilibrium hypsometry, tidal flats, alternating bars, channel meandering, channel bifurcation<br />
* [[Estuary response to sea-level rise]]<br />
* [[Estuary channelization]] - impact on hydrodynamics, salt intrusion, sedimentation, turbidity, field cases, modelling<br />
* [[Tidal flat reclamation]] – morphodynamic response, consequences for physical and ecological processes in estuaries and options for restoration <br />
* [[ICZM issues in estuaries]] <br />
* [[Bio-geomorphology of salt marshes]] – landscape dynamics of salt marshes resulting from the interaction between biotic and physical processes <br />
<br />
<br />
'''External references'''<br />
* [https://ozcoasts.org.au/conceptual-diagrams/science-models/geomorphic/ OzCoast Deltas]<br />
<br />
<br />
<br />
===Coastal morphology measuring techniques===<br />
<br />
'''Coastal Wiki articles'''<br />
* [[Bathymetry from inverse wave refraction]] <br />
* [[Data processing and output of Lidar]]<br />
* [[Hyperspectral seafloor mapping and direct bathymetry calculation in littoral zones]]<br />
* [[Instruments for bed level detection]]<br />
* [[Space geodetic techniques for coastal zone monitoring]]<br />
* [[Argus applications]]<br />
* [[Argus image types and conventions]]<br />
* [[Argus standard image processing]]<br />
* [[Argus video]]<br />
* [[Argus video monitoring system]]<br />
* [[Data analysis techniques for the coastal zone]]<br />
<br />
<br />
<br />
===Coastal morphodynamic modelling and self-organisation===<br />
<br />
'''Coastal Wiki articles'''<br />
* [[Stability models]]<br />
* [[Rhythmic shoreline features]] <br />
* [[Beach Cusps]]<br />
* [[Sand ridges in shelf seas]]<br />
* [[Process-based modelling]]<br />
* [[Process-based morphological models]] <br />
* [[Geomorphological analysis]] <br />
* [[Behaviour-based models]] <br />
* [[Littoral drift and shoreline modelling]] <br />
* [[Stochastic and fractal methods in coastal morphodynamics]]<br />
<br />
<br />
'''Coastal Wiki gaps''' <br />
* [[Coastline instability]] - introduction to conditions for coastline instability, occurrence, characteristics of unstable coastlines, observations, processes, morphodynamic feedback, modelling, practical formulas, implications for coastal management<br />
* [[Nearshore bed forms and bed roughness]] – extension of [[Bedforms and roughness]] with a more detailed treatment of the physical background and practical methods for representing the influence of bed forms and bed roughness in the nearshore zone in numerical models of waves, currents, mixing and sediment transport<br />
* [[Sand waves]] - introduction to characteristics of sand waves, their practical importance, conditions and major (feedback)processes for their formation, evolution and maintenance, modelling, some examples and simple rules<br />
* [[Bio-geomorphology of the coastal zone]] – morphological and ecological patterns in the coastal zone resulting from the interaction between biotic and physical processes<br />
<br />
===Coastal erosion===<br />
<br />
'''Coastal Wiki articles'''<br />
* [[Bruun rule for shoreface adaptation to sea-level rise]] <br />
* [[Types and background of coastal erosion]] <br />
* [[Natural causes of coastal erosion]]<br />
* [[Human causes of coastal erosion]] <br />
* [[Accretion and erosion for different coastal types]] <br />
* [[Port breakwaters and coastal erosion]]<br />
* [[Dune erosion]]<br />
* [[Coastal Erosion along the Changjiang Deltaic Shoreline]]<br />
* [[Dealing with coastal erosion]]<br />
* [[Shoreline management]]<br />
<br />
<br />
'''Coastal Wiki gaps''' <br />
* [[Shoreline prediction]] – practical (data-driven) methods, applicability, storms, implication for coastal management<br />
* [[Decadal coastal prediction]] - introduction to (data-driven) methods for predicting coastal evolution over decadal time scale<br />
<br />
<br />
===Long-term morphodynamics and climate change===<br />
<br />
'''Coastal Wiki articles'''<br />
* [[Sea level rise]]<br />
* [[Geomorphological time scales and processes]]<br />
* [[Effect of climate change on coastline evolution]] <br />
* [[Bruun rule for shoreface adaptation to sea-level rise]] <br />
* [[Potential Impacts of Sea Level Rise on Mangroves]]<br />
* [[Ocean circulation]]<br />
* [[Thermohaline circulation of the oceans]]<br />
<br />
<br />
'''Incomplete articles'''<br />
* [[Geomorphology]] – needs expansion to a general article linking to more specific articles<br />
* [[Climate change]] - extend existing definition to general introduction to the topic<br />
<br />
<br />
'''Coastal Wiki gaps''' <br />
* [[Climate change impacts]] general article with links to more specific articles, and to articles on sea level change<br />
* [[Stratigraphy of coastal systems]] – introduction to depositional/erosional seabed structures, relation with depositional and erosional processes, long-term morphodynamic processes, response to sea-level rise <br />
* [[Long-term coastal evolution]] - introduction to evolution of sedimentary coasts during the Holocene, processes and interactions, modelling, response to future sea-level rise, implications for coastal management<br />
* [[Quaternary geology]] - glaciology, case studies, saltmarsh climate change dating<br />
* [[Sea level change]] - indications of former sea levels, causes of sea level change, pleistocene, holocene, present, future, isostacy and eustacy, tectonics, climate change<br />
* [[Geomorphological modelling]] at geological time scale <br />
* [[Seawater intrusion in coastal aquifers]]<br />
* [[ICZM issues associated with long term geomorphology]]<br />
<br />
<br />
<br />
== Coastal protection and engineering ==<br />
<br />
===Hard measures===<br />
* [[Hard coastal protection structures]]<br />
* [[Groynes]]<br />
* [[Groynes as shore protection]]<br />
* [[Deteriorated groynes]] <br />
* [[Detached breakwaters]] <br />
* [[Applicability of detached breakwaters]] <br />
* [[Detached shore parallel breakwaters]] <br />
* [[Application of breakwaters]]<br />
* [[Revetments]]<br />
* [[Seawalls and revetments]] <br />
* [[Overtopping resistant dikes]]<br />
* [[Bulkheads]]<br />
<br />
===Soft measures===<br />
* [[Artificial reefs]] <br />
* [[Natural barriers]] <br />
* [[Dynamics, threats and management of biogenic reefs]]<br />
* [[Sand-filled geosystems in coastal engineering]]<br />
* [[Beach nourishment]] <br />
* [[Artificial nourishment]] <br />
* [[Shore nourishment]] <br />
* [[Experiences with beach nourishments in Portugal ]] <br />
* [[Floating breakwaters]] <br />
* [[Perched beaches]] <br />
* [[Beach drainage]]<br />
* [[Sand by-pass systems]]<br />
* [[Sand dune types - Europe]] <br />
* [[Dynamics, threats and management of dunes]] <br />
<br />
===Wind and wave energy===<br />
* [[Wave energy converters]]<br />
* [[Wave energy converters in coastal structures]]<br />
* [[Offshore wind farm development in Germany]]<br />
<br />
<br />
'''Incomplete articles'''<br />
* [[Dredging]] needs expansion with overview article of techniques and impact<br />
<br />
<br />
'''Coastal Wiki gaps''' <br />
* [[Experience with coastal nourishment in the Netherlands]]<br />
* [[Coastal defence options]] - UK MAFF guidelines, do nothing, risk management, sustain, change<br />
* [[Resonance phenomena]] - dealing with seiches in harbours and basins<br />
* [[Disposal of dredged materials]] – including fate of dredged materials<br />
* [[Use of mud in coastal structures]]<br />
* [[Sand mining in shelf seas]] - introduction to sand mining strategies (surface/depth of pits, frequency), impact on hydrodynamics, morphological evolution, ecological recovery, good practice guidelines<br />
* [[Estuary engineering]] - deepening and channelisation of estuaries, tidal flat reclamation, impacts, coastal squeeze, managed realignment. (See also [<br />
* [[Tidal power]] – introduction to methods for tidal energy exploitation, practical experience<br />
* [[Marine wind energy]] introduction to methods and conditions for sustainable and efficient exploitation (technical, financial, environmental)<br />
* [[Examples of marine wind farms]] – practical experience <br />
<br />
<br />
'''External references'''<br />
* [http://deltaproof.stowa.nl/pdf/Sand_nourishments?rId=53 Sand nourishment]<br />
* [http://deltaproof.stowa.nl/pdf/The_beneficial_re_use_of_dredged_material?rId=52 Reuse of dredged material]<br />
* [http://deltaproof.stowa.nl/pdf/Managed_realignment?rId=51 Managed realignment]<br />
<br />
<br />
<br />
<br />
[[Category:Coastal protection]]<br />
[[Category:Physical coastal and marine processes]]</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Dam_break_flow&diff=76334Dam break flow2020-01-15T20:21:20Z<p>Dronkers J: </p>
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<div><br />
This article discusses the often catastrophic flows that result from the failure of high dams that protect low-lying land. Dam break mechanisms are not dealt with; for this the reader is referred to the extensive literature existing on this subject, see for example Zhang et al. (2016) <ref>Zhang, L., Peng, M., Chang, D. and Xu, Y. 2016. Dam failure and Risk Assessment. John Wiley and Sons, Singapore</ref> and Almog et al. (2011) <ref>Almog, E., Kelham, P and King, R. 2011. Modes of dam failure and monitoring and measuring techniques. Environmental Agency,UK https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/290819/scho0811buaw-e-e.pdf</ref>.<br />
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<br />
==Introduction==<br />
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[[image:Dijkdoorbraak1953.png|thumb|left|300px|Fig. 1. Sea dikes protecting low-lying polders in the Netherlands were breached during the extreme storm surge of 31 January 1953.]] <br />
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Dam failure can lead to disastrous situations. Most dam break tragedies are related to the collapse of reservoir dams in mountain rivers. The failure of sea dikes can also cause major disasters, although in this case the level difference is not as large. A dramatic example is the failure of more than fifty sea dikes in the Netherlands during the extreme storm surge of 1953, see figure 1. Many of these dikes protected land lying below the average sea level, while the storm surge level exceeded more than five meters. Rapid flooding killed more than two thousand people who were unable to flee in time to safe places. The most common dam failure mechanisms are related to overtopping and seepage (also called piping or internal erosion)<ref name=F8>Froehlich, D.C. 2008. Embankment Dam Breach Parameters and Their Uncertainties. Journal of Hydraulic Engineering, ASCE 134: 1708-1721</ref>. In the case of the 1953 storm surge, overtopping and subsequent scour of the interior dike slope was the most important dike failure mechanism. <br />
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[[image:DamBreakFlowPrinciple.jpg|thumb|center|600px|Fig. 2. Left panel: Schematic representation of water retention behind a dam. Right panel: Positive downstream and negative upstream surges following instantaneous dam removal.]]<br />
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<br />
The consequences of dam failure have been studied for more than a century. It nevertheless remains a challenging topic due to the high non-linearity of the flood wave propagation. The problem can be tackled with numerical models, but rough estimates and insight into the tidal wave dynamics can be obtained with analytical solution methods.<br />
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<br />
==Frictionless dam-break flow: analytical solution==<br />
<br />
Analytical solutions relate to idealized situations as depicted in Fig. 2. The initial situation consists of an infinite reservoir with a water level that is <math> h_0 </math> higher than the horizontal ground level downstream of the dam. Dam break is simulated by instantaneous removal of the dam. This causes a positive surge in the positive <math> x </math>-direction and a negative surge in the negative <math> x </math>-direction. The floor is dry in front of the positive surge and the body of water behind the negative surge is undisturbed: water level =<math> h_0 </math> and current speed <math> u = 0 </math>.<br />
<br />
[[image:SouthForkDamFailure1889.jpg|thumb|left|300px|Fig. 3. The earth-filled South Fork Dam on Lake Conemaugh (Pennsylvania, US) collapsed in 1889, killing 2,209 people in downstream villages.]]<br />
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The study of the dam break-flow was triggered by several dam failures in the 19th century, in particular the breach of the South Fork Dam in Pennsylvania (USA) in 1889, Fig. 3. Three years later Ritter <ref> Ritter, A. 1892. Die Fortpflanzung der Wasserwellen. Zeitschrift des Vereines Deutscher Ingenieure 36: 947-954 </ref> published an exact analytical solution for dam-break flow by assuming that frictional effects can be ignored. The derivation is given in box 1. According to this solution, the tip of the positive surge advances at high speed (supercritical flow) given by <math> u_f = 2 c_0</math>, where <math>c_0 = \sqrt {gh_0}</math> and <math> g </math> is the gravitational acceleration. The shape of the positive and negative wave is a concave-up parabola,<br />
<br />
<math>h(x,t)= h_0, \; x<-c_0 t; \quad h(x,t)= \Large\frac{h_0}{9}\normalsize \; (2 - \Large\frac{x}{c_0 t}\normalsize)^2 , \, -c_0 t<x<2c_0 t; \quad h(x,t)= 0, \, x>2c_0 t , \qquad (1)</math><br />
<br />
see Fig. 4. According to Eq. (1) and Box 1, the discharge through the breach per unit width is given by<br />
<br />
<math>q = \frac{8}{27} h_0 \sqrt{g h_0}. \qquad (2) </math> <br />
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Figure 4 also shows the shape of the dam break wave that was observed in laboratory experiments. For small values of <math> x / t </math>, the frictionless solution corresponds fairly well with the observations. However, the front zone is different: the shape is a bull nose, rather than a sharp edge. The front also advances more slowly; the speed of the front decreases with time and is closer to <math> u_f = c_0 </math> than to <math> u_f = 2 c_0 </math>. The reason for this difference is the neglect of frictional effects that are important in the thin fluid layer near the front.<br />
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[[image:DamBreakFlowDerivation.png|thumb|center|900px|Box 1. Derivation of the solution for frictionless dam break flow.]]<br />
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==Dam-break flow with friction==<br />
<br />
[[image:DamBreakWaveProfiles.jpg|thumb|left|400px|Fig. 4. Wave profile after dam break. The red curve corresponds to the frictionless solution Eq. 1. The blue band represents data from different laboratory experiments performed at times <math>\small t \sim (40-80) \, \sqrt {h_0 / g}\normalsize </math> after removal of the dam <ref>Dressler, R. 1954. Comparison of theories and experiments for the hydraulic dam-break wave. Proc. Int. Assoc. Scientific Hydrology Assemblée Générale, Rome, Italy 3 (38)M 319–328</ref> <ref>Schoklitsch, A. 1917. Über Dambruchwellen. Kaiserliche Akademie der Wissenschaften, Wien, Mathematisch-Naturwissenschaftliche Klasse, Sitzungberichte IIa, 126: 1489–1514</ref><ref>Cavaillé,Y. 1965. Contribution à l’étude de l’écoulement variable accompagnant la vidange brusque d’une retenue. Publ. Scient. et Techn. du Ministère de l’Air, 410, Paris, France, 165</ref>. The frictionless solution only depends on <math>x/t</math>. Observed wave profiles also depend on time <math>t</math> because of the decreasing wave tip speed.]]<br />
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When friction terms are included in the flow equations, there is no exact analytical solution. It is generally assumed that the frictionless flow equations are approximately valid in a short period after dam break and for small values of <math>x / (c_0 t) </math>. In the front zone, where the water depth is small, the momentum balance is dominated by frictional momentum dissipation. If the inertia terms <math>\partial u / \partial t + u \partial u / \partial x </math> in the momentum equation are ignored, then the current in the front region is mainly determined by the balance of gravitational acceleration <math> g \partial h / \partial x </math> and shear stress <math>\tau</math>, the latter term being proportional to the square of the flow velocity<ref>Dressler, R.F. 1952. Hydraulic resistance effect upon the dambreak functions. J. Res. Natl. Bureau of Standards, 49(3): 217–225</ref><ref>Whitham, G.B. 1955. The effects of hydraulic resistance in the dam-break problem. Proc. Roy. Soc. of London, Serie A, 227: 399–407</ref><ref>Hogg, A.J. and Pritchard, D. 2004. The effects of hydraulic resistance on dam-break and other shallow inertial flows. J. Fluid Mech. 501: 179–212</ref><ref name=C09>Chanson, H. 2009. Application of the method of characteristics to the dam break wave problem. Journal of Hydraulic Research 47: 41–49</ref>. With such models the shape of the wave front is given by <math>h(s) \propto s^n, \; n=1/2</math>, where <math>s</math> is the distance measured from the wave front. The wave front speed <math>u_f</math> decreases with time. At large times <math>t>>t_{\infty}</math>, the wave front speed varies approximately as <math>u_f \approx c_0 \sqrt{t_{\infty}/t}</math> <ref name=C09></ref>. Here, <math>t_{\infty} = \sqrt{h_0/g}/(3 c_D)</math> and <math>c_D</math> is the friction coefficient (value in the range <math>\approx (1-5)\, 10^{-3}</math>). A more elaborate model of the frictional boundary layer near the wave front was studied by Nielsen (2018) <ref name=PN>Nielsen, P. 2018 Bed shear stress, surface shape and velocity field near the tips of dam-breaks, tsunami and wave runup velocity. Coastal Engineering 138: 126–131</ref>. According to this model, the wavefront is even more blunt, corresponding to <math> n = 1/4 </math>, which agrees well with laboratory experiments. This model also reveals a strong downward velocity component at the wavefront, which can contribute to the dislodging of particles from the sediment bed <ref name = PN> </ref>. This may explain the high near-bed of suspended concentrations associated with propagating surges observed in the field<ref>Khezri, N. and Chanson, H. 2012. Inception of bed load motion beneath a bore. Geomorphology 153: 39–47</ref>, see also the article [[Tidal bore dynamics]]. <br />
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Data from numerous reservoir dam breaks that have occurred in the past have provided empirical formulas for the maximum discharge <math>Q_{max}</math> through the breach <ref>Froehlich, D.C. 2016. Predicting Peak Discharge from Gradually Breached Embankment Dam. Journal of Hydraulic Engineering, ASCE 04016041</ref><ref name=W> Wang, B., Chen, Y., Wu, C., Peng, Y., Song, J., Liu, W. and Liu, X. 2018. Empirical and semi-analytical models for predicting peak outflows caused by embankment dam failures. Journal of Hydrology 562: 692–702</ref>. From this data it was deduced that the width of the breach is mainly related to the volume of water <math>V</math> in the reservoir (volume above breach level). A reasonable estimate of the width is given by <ref name=F8></ref> <math> B \approx 0.3 V ^ {1/3} </math>. Empirical formulas for the maximum dam break discharge then yield <ref>Webby, M. G. 1996. Discussion of ‘Peak outflow from breached embankment dam.’ by D. C. Froehlich. J. Water Resour. Plann. Management 122:4(316), 316–317</ref> <ref name=W></ref><br />
<br />
<math>Q_{max} \approx 0.04 \sqrt{g} \, V^{0.37} h_0^{1.4} \approx 0.15 h_0 \, B \, \sqrt{g h_0} \, V^{0.04} h_0^{-0.1} , \qquad (3)</math> <br />
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or<br />
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<math> q_{max} \approx 0.22 h_0 \, \sqrt{g h_0} , \qquad (4)</math><br />
<br />
where in the approximation for the maximum discharge per unit width we have considered a large reservoir volume (<math>V \approx 10^7 m^3</math>) and a water depth <math>h_0 \approx 15 m</math>. The empirical estimate (4) is about 75% of the estimate (2) given by the frictionless flow solution.<br />
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==Numerical models==<br />
<br />
The analytical methods for describing dam-break flow provide a qualitative picture and some first-order estimates for the wave profile and wave speed. They may only be used in situations that can be represented schematically by a simple prismatic channel. In most actual field situations, the dam-break flow must be modeled numerically. Detailed simulation of the forward and backward wave fronts requires 3D models of the Boussinesq type, taking into account vertical fluid accelerations<ref>Castro-Orgaz, O. and Chanson, H. 2017. Ritter’s dry-bed dam-break flows: positive and negative wave dynamics. Environ Fluid Mech (2017) 17:665–694</ref>. To correctly model the strong temporal and spatial gradients of the surging wave, a fine computational grid is required, with resulting long computer times. See also [[Tidal bore dynamics]]. <br />
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==References==<br />
<references/><br />
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{{author<br />
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[[Category:Physical coastal and marine processes]]<br />
[[Category:Hydrodynamics]]<br />
[[Category:Coastal protection]]</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Tidal_bore_dynamics&diff=76333Tidal bore dynamics2020-01-15T20:19:03Z<p>Dronkers J: </p>
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<div><br />
==Introduction==<br />
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A tidal bore is a sudden elevation of the water surface that travels upstream an estuary with the incoming flood tide. This article describes the processes involved in this ultimate stage of tidal wave deformation and the modelling of these processes. For an introduction to the topic of tidal wave deformation the reader is referred to the article [[Tidal asymmetry and tidal basin morphodynamics]].<br />
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[[Image:DordogneTidalBore.jpg|center|700px|thumb|Figure 1. Left image : Partially breaking tidal bore on the Dordogne River (Courtesy of Antony “YEP” Colas). Right image : Undular tidal bore on the Garonne River (Bonneton et al. 2011 <ref name=B11a>Bonneton, P, Parisot, J-P., Bonneton, N., Sottolichio, A., Castelle, B., Marieu, V., Pochon, N. and Van de Loock, J. 2011. Large amplitude undular tidal bore propagation in the Garonne River, France, Proceedings of the 21st ISOPE Conference: 870-874, ISBN 978-1-880653-96-8</ref>).]]<br />
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|+ Table 1. Estuaries and rivers with substantial tidal bores (bore height of half a meter up to several meters). The maximum tidal range is the maximum range recorded at a tide gauge situated close to the location in the estuary where the tidal range is highest. <br />
|- style="font-weight:bold; font-size: 11px; text-align:center; background:lightblue" <br />
! width="25% style=" border:1px solid blue;"| Estuary/river name<br />
! width="5% style=" border:1px solid bleu;"| Maximum tidal range [m]<br />
! width="20% style=" border:1px solid blue;"| Tide gauge location<br />
! width="10% style=" border:1px solid blue;"| Country<br />
|- <br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Shannon River<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| 5.6<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Shannon<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Ireland<br />
|-<br />
| style="border:2px solid lightblue; font-size: 10px; font-size: 10px; font-size: 10px; text-align:center"| Humber,Trent<br />
| style="border:2px solid lightblue; font-size: 10px; font-size: 10px; text-align:center"| 8.3<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Hull<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center" rowspan="8"| UK<br />
|- <br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Great Ouse<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| 7.4<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| King's Lynn<br />
|- <br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Severn<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| 12<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Portishead<br />
|-<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Dee<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| 9.8<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Flint<br />
|- <br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Mersey<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| 10<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Liverpool<br />
|- <br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Ribble<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| 10.2<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Lytham<br />
|-<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Morecambe bay, River Kent<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| 10.9<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Morecambe<br />
|-<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| River Eden, Nith River <br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| 10.3<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Silloth<br />
|-<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Seine <br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| 8.5<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Honfleur<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center" rowspan="4"| France<br />
|- <br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Canal de Carentan<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| 7<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Carentan<br />
|- <br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Baie du Mont Saint Michel – Sélune River<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| 14<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Granville<br />
|- <br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Garonne, Dordogne<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| 6.3<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Podensac<br />
|- <br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Pungue<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| 7<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Beira<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Mozambique<br />
|- <br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Qiantang<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| 5<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Ganpu<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| China<br />
|- <br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Indus <br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| 4<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Port Muhammad Bin Qasim<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Pakistan<br />
|- <br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Hooghly<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| 5.7<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Sagar Island<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| India<br />
|- <br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Brahmaputra<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| 5.7<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Chittagong<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Bangladesh<br />
|- <br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Sittaung<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| 6.3<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Moulmein<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Myanmar<br />
|-<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Batang Lupar River<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| 5.6<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Kuching<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Sarawak<br />
|-<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Kampar River<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| 5.3<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Pulo Muda<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Sumatra<br />
|-<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Hooghly<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| 5.7<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Sagar Island<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| India<br />
|-<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Fly , Bamu, Turamu , Mappi Rivers<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| 4.2<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| estuary <br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| West Papua <br />
|-<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Styx<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| 6.4<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Mackay, Queensland<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center" rowspan="2"| Australia <br />
|-<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Daly River<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| 7.9<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| estuary<br />
|-<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Turnagain Arm, Knick Arm<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| 7.9<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Anchorage<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Alaska<br />
|-<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Bay of Fundy, Petitcodiac and Salmon rivers<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| 16<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Truro<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Canada<br />
|-<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Colorado River<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| 7.7<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| San Filipe<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Mexico<br />
|-<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Amazon, Araguira, Guama, Capim and Mearim Rivers<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| 3.4<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Macapa<br />
| style="border:2px solid lightblue; font-size: 10px; text-align:center"| Brazil<br />
|}<br />
<br />
<br />
==Occurrence of tidal bores==<br />
<br />
When a tidal wave propagates upstream into an estuary, its shape is progressively distorted. In many estuaries the high-water (HW) tidal wave crest propagates faster up-estuary than the low-water (LW) tidal wave trough. HW propagates considerably faster than LW if the mean channel depth <math>D_0</math> is not much greater than the spring tidal range <math>2a</math> (same order of magnitude or a few times larger) and if the intertidal area is not much greater than the tidal channel surface area. The tidal rise period is shortened and the tidal wave becomes steeper during propagation. If the tidal wave can propagate sufficiently far upstream the river without strong damping, the tidal wave front may become so steep that a water level jump – a so-called tidal bore - can form at the beginning of the rising tide. <br />
<br />
Table 1 presents estuaries and tidal rivers in which significant tidal bores have been observed (a more complete overview can be found in Bartsch-Winkler and Lynch (1988) <ref> Bartsch-Winkler, S., and Lynch, D. K. 1988. Catalog of worldwide tidal bore occurrences and characteristics. US Government Printing Office</ref> and a recently updated catalog by Colas (2017)<ref> Colas, A. 2017. Mascaret, prodige de la marée. Atlantica Editions</ref>). It appears that tidal bores generally occur for large tidal ranges (<math>Tr_0</math>) at the estuary mouth. However, such a simple criterion is not sufficient to classify estuaries in terms of tidal bore occurrence. For instance, Furgerot (2014) <ref name=Fu14>Furgerot, L. (2014). Propriétés hydrodynamiques du mascaret et de son influence sur la dynamique sédimentaire: Une approche couplée en canal et in situ (estuaire de la Sée, Baie du Mont Saint Michel) (Doctoral dissertation, Caen)</ref> showed that in the Sée/Mont Saint Michel estuary, <math>Tr_0</math> must be larger than 10 m for tidal bore formation in the Sée River and, on the other hand, Bonneton et al. (2015)<ref name=B15> Bonneton, P., Bonneton, N., Parisot, J-P. and Castelle, B. 2015. Tidal bore dynamics in funnel-shaped estuaries. J. Geophys. Res.: Ocean 120: 923-941. DOI: 10.1002/2014JC010267</ref> observed tidal bores in the Gironde/Garonne estuary even for <math>Tr_0</math> smaller than 2 m. <br />
<br />
The estuarine shape (depth and width profiles) plays an important role in tidal bore formation. This is illustrated by the observation that regulation works (dredging, reclamation, weirs) during the past century have weakened or even completely suppressed tidal bores in many rivers, for example in the rivers Seine, Charente, Colorado and Petitcodiac. We will discuss in the following general conditions for bore formation in terms of estuary geometry and flow conditions. g<br />
<br />
Illustrations of tidal bores are shown in Fig. 1.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
==Tidal bore formation in funnel-shaped estuaries==<br />
<br />
The analysis of nonlinear tidal wave transformation in estuaries, in terms of tidal forcing at the estuary mouth and large-scale geometrical properties of the channel, has received considerable attention (see [[Tidal asymmetry and tidal basin morphodynamics]]). By contrast, the extreme nonlinear tidal-wave case where tidal bores form is much less studied. <br />
<br />
The most intense tidal bores occur in long and shallow tide-dominated funnel-shaped estuaries (e.g. Qiantang, Severn, Kampar, Gironde/Garonne/Dordogne, …) . The formation of these tidal bores is governed by the progressive distortion of the tidal wave as it propagates up the estuary. If the ebb-flood asymmetry (duration of falling tide longer than rising tide and larger flood than ebb currents) is strong enough, a tidal bore can form in the upper estuary. This is illustrated by the tidal asymmetry in the Garonne at Bordeaux (Fig. 2) and the upstream tidal bore at Podensac (Fig.3). <br />
<br />
This extreme nonlinear deformation of a tidal wave occurs in a limited number of estuaries. To determine the conditions favourable to tidal bore occurrence, a scaling analysis can be carried out for a schematic channel geometry. A usual schematization is based on the approximations <ref>Lanzoni, S. and Seminara, G. 1998. On tide propagation in convergent estuaries, J. Geophys. Res. 103: 30793–30812</ref><ref name=S>Savenije, H.H.G. 2012. Salinity and Tides in Alluvial Estuaries, second ed., Salinity and Tides in Alluvial Estuaries, second ed., www.salinityandtides.com</ref><ref>Dronkers, J. 2017. Convergence of estuarine channels. Continental Shelf Res. 144: 120–133</ref>:<br />
*Uniform channel depth <math>D</math>,<br />
*Exponential convergence of the width <math>B(x)</math>.<br />
The convergence length <math>L_b </math>, defined as <math>L_b=B(x)/dB/dx</math>, is assumed independent of the along-channel coordinate <math>x</math>. <br />
The forcing tidal wave at the estuary mouth can be characterized by its tidal frequency <math>\omega=2 \pi / T</math> and its amplitude <math>A_0=Tr_0/2</math>, where <math>Tr_0</math> is the estuary mouth tidal range. Another important parameter which influences tidal propagation in an estuary is the dimensionless mean friction coefficient <math>c_D</math>. The tidal wave dynamics is then controlled, if we neglect fresh water discharge effects, by three dimensionless parameters: <br />
*the nonlinearity parameter, <math>\epsilon=A_0/D</math>,<br />
*the friction parameter, <math>\phi=c_D \sqrt{gD}/(\omega D)</math>,<br />
*the convergence ratio, <math>\delta=\sqrt{gD}/(\omega L_b)</math>.<br />
<br />
<br />
[[Image:GaronneObservationOndularBoreDevelopment.jpg |center|800px|thumb|Figure 2. Tidal wave distortion and bore formation observed in the Gironde-Garonne estuary (Bonneton et al. 2015<ref name=B15></ref>) at spring tide. Left panel: Tide gauge locations on the estuary. Right top panel: Time series of tide elevation at 4 different locations, from the estuary mouth (Le Verdon) to the upper estuary (Podensac); Right bottom panel: Tidal bore illustrations at Podensac field site, located 126 km upstream the river mouth.]]<br />
<br />
[[Image:TidalBoreSimulation.jpg |center|600px|thumb| Figure 3. Tidal wave distortion and bore formation in a convergent estuary. Numerical simulations by Filippini et al. 2019 <ref name=F> Filippini, A. G., Arpaia, L., Bonneton, P., & Ricchiuto, M. 2019. Modeling analysis of tidal bore formation in convergent estuaries. European Journal of Mechanics-B/Fluids 73: 55-68</ref>. Left panel: Rising tide elevation at different increasing times. Right panel: Zoom of left panel.]]<br />
<br />
<br />
The formation of tidal bores is mainly governed by the progressive distortion of the tidal wave as it propagates up the estuary. This extreme nonlinear deformation of the tidal wave occurs under special conditions, in particular<ref name=B15></ref> <ref name=R>Rousseaux, G., Mougenot, J. M., Chatellier, L., David, L. and Calluaud, D. 2016. A novel method to generate tidal-like bores in the laboratory. European Journal of Mechanics-B/Fluids 55:31-38</ref>: <br />
*a large tidal amplitude <math>a</math>, <br />
* a long, shallow and convergent channel.<br />
<br />
[[Image:BoreFormationCondition.jpg|left|400px|thumb|Figure 4. Estuarine classification in parameter space (<math>\epsilon, \phi</math>). Maximum surface elevation slope <math>A_{max}</math>, the white dashed line represents the <math>\epsilon_c</math> curve, namely the limit for tidal bore appearance following the criterion <math>A_{max} \ge 10^{-3}</math>. Each point in the plane (<math>\epsilon, \phi</math>) represents a numerical tidal wave solution for an idealized convergent estuary; this figure relies on 225 numerical simulations (Filippini et al., 2019)<ref name=F></ref>.]]<br />
<br />
Available field data suggest that tidal bores form in convergent estuaries characterized by large values of the convergence ratio <math>\delta</math>. Bonneton et al. (2016)<ref name=B16> Bonneton, P., Filippini, A.G., Arpaia, L., Bonneton, N. and Ricchiuto, M. 2016. Conditions for tidal bore formation in convergent alluvial estuaries. Estuarine, Coastal and Shelf Science. 172: 121-127</ref> and Filippini et al. (2018)<ref name=F></ref> have analysed tidal bore occurrence as a function of the dimensionless parameters <math>\epsilon</math> and <math>\phi</math> for a fixed value of the convergence ratio <math>\delta=2.4</math>. Fig. 4 presents the position of convergent estuaries in the parameter space (<math>\epsilon, \phi</math>). We can observe a clear separation between tidal-bore estuaries and non tidal-bore estuaries. Tidal bores occur when the nonlinearity parameter <math>\epsilon</math> is greater than a critical value, <math>\epsilon_c</math>, which is an increasing function of the friction parameter <math>\phi</math>. For small <math>\phi</math>-values (friction parameter <math>\phi \approx 15</math>), tidal bores can form for <math>\epsilon</math> greater than 0.2. By contrast, for large <math>\phi</math>-values the tidal bore formation requires much larger nonlinearity parameters. These results show that bore formation is mainly controlled by the competition between two physical processes: (a) the nonlinear distortion of the tidal wave, which is favourable to bore inception; (b) the friction dissipation of the tidal wave, which is unfavourable to bore formation. <br />
<br />
<br />
==Conditions for tidal bore formation==<br />
<br />
More generally, the analysis of tidal bores observed in natural estuaries suggests the following conditions for tidal bore formation.<br />
<br />
The first requirement for tidal bore formation is sufficient length of the estuarine-tidal river system, i.e. the tide can penetrate far enough into the system. This depends primarily on the average longitudinal slope of the estuary-tidal river system, with a secondary role for the convergence length <math>L_b</math>. A steep slope limits the penetration of the tide. A small channel slope is generally indicative of low-to-moderate current velocities and friction (steep slopes are generally related to strong friction generated by high current velocities and coarse bed sediments). If the longitudinal channel slope is small, the tidal bore can travel over a long distance without much dissipation.<br />
<br />
The tidal bore develops in a section of the estuary-tidal river system where the nonlinearity parameter <math>\epsilon</math> is large (shallow depth, large tidal range) and where the tidal wave is flood-dominant. Sometimes a tidal bore already forms close to the mouth of the estuary. This is the case with estuaries that have a large mouth bar, such as the Qiangtang estuary and the Charente estuary (the latter before large-scale interventions took place). But this is rather the exception. Most often the tidal bore is formed in a section of the estuary-tidal river system further upstream, in the tidal river or on the tidal flats at the head of the estuary (as for the Garonne, Seine, Sée, etc.). <br />
<br />
The condition of a large tidal range and a strong tidal asymmetry depends on friction; one should therefore distinguish between muddy and sandy/gravelly estuaries. If the solid fluvial flow is important with a large fraction of cohesive mud (mainly estuaries in the (sub) tropic regions, but also the Garonne) the estuarine channel bed is smooth so that the friction is weak (small <math>\phi</math>); the tidal wave is not strongly damped. In this case a small relative channel depth (large <math>\epsilon</math>) is the main condition to obtain a strong asymmetry of the tidal wave. Rivers with low solid discharge or supplying sandy/coarse sediments have a sandy or gravelly channel bed in the estuarine zone that produces strong friction (large <math>\phi</math>) and strong tidal energy dissipation. In this case, strong convergence of the width of the estuary (large <math>\delta</math>) is required to generate a large, highly asymmetric tidal amplitude (large <math>\epsilon</math>).<br />
<br />
River flow also influences tidal bore formation. River flow contributes to tidal wave deformation by enhancing the longitudinal velocity gradient. However, river flow also contributes to tidal wave damping and thus opposes tidal bore formation <ref name=H> Horrevoets, A. C., Savenije, H. H. G., Schuurman, J. N. and Graas, S. 2004. The influence of river discharge on tidal damping in alluvial estuaries. Journal of Hydrology 294: 213-228</ref>. The latter effect usually dominates. Observations show that the tidal bore in the Garonne and Dordogne (France) is suppressed at high river runoff<ref name=B16>Bonneton, P., Filippini, A.G., Arpaia, L., Bonneton, N. and Ricchiuto, M. 2016. Conditions for tidal bore formation in convergent alluvial estuaries. Estuarine, Coastal and Shelf Science. 172: 121-127</ref>. For large discharge (order of 1000 m3/s), tidal bores do not form. By contrast, for low discharge (order of 150 m3/s) a tidal bore almost always occurs in the Garonne River, even at neap tide. These findings were confirmed by Filippini et al. (2019)<ref name=F></ref> from numerical simulations. A similar effect is observed in the Daly estuary by Wolanski et al. (2004)<ref> Wolanski, E., Williams, D., Spagnol, S. and Chanson, H. 2004. Undular tidal bore dynamics in the Daly Estuary,Northern Australia. Estuarine, Coastal and Shelf Science 60: 629-636</ref>, who relate the occurrence of the tidal bore at low river discharge to the small water depth during such conditions. However, the opposite effect is reported for the Guamá-Capim river system near the mouth of the Amazon River, where tidal bores are observed only at high river discharges, in conjunction with high equinoctial tides<ref name=F>Freitas, P.T.A., Silveira, O.F.M. and Asp, N.E. 2012. Tide distortion and attenuation in an Amazonian tidal river. Brazilian journal of oceanography, 60: 429-446</ref>. <br />
<br />
Variations in local river geometry and water depth can also significantly affect tidal bore dynamics (Bonneton et al. (2011)<ref name=B11a></ref> and Keevil et al. (2015)<ref>Keevil, C. E., Chanson, H. and Reungoat, D. 2015. Fluid flow and sediment entrainment in the Garonne River bore and tidal bore collision. Earth Surface Processes and Landforms 40: 1574-1586</ref>). Observations show that tidal bores often develop in shallow rivers that discharge from the higher upstream zone into a broad estuary. If the tidal wave has already acquired sufficient asymmetry when travelling through the estuary, a tidal bore develops when the tidal wave surges into the shallow river. The presence of a mouth bar (large <math>\epsilon</math>) is favourable to the development of strong asymmetry of the tidal wave and tidal bore formation, see Fig. 5. On the contrary, the presence of local channel width constrictions (large <math>\phi</math>) is unfavourable to tidal bore formation, as illustrated by the absence of a tidal bore in the Conway estuary in spite of a high non-linearity parameter. <br />
<br />
<br />
[[Image:Seine-Qiangtang.jpg|center|700px|thumb|Figure 5. Many natural estuaries have large shoals in the mouth zone. These so-called mouth bars strongly enhance distortion of the tidal wave entering the estuary. Left image: Tidal bore in the Seine River around 1960, before the mouth bar was dredged. Right image: Tidal bore in the Qiangtang estuary, where a large mouth bar is still present (https://en.wikipedia.org/wiki/Qiantang_River ).]]<br />
<br />
<br />
==Tidal bore characteristics==<br />
<br />
A tidal bore can be schematically represented by a propagating transition between two streams of water depth <math>D_1</math> and <math>D_2</math>, with <math>D_1 < D_2</math> (see Fig. 6). Once such a hydraulic jump has developed, its flow velocities ahead and behind the jump can be derived from the mass and momentum balance equations (Fig. 6):<br />
<br />
[[Image:TidalBorePropagation.jpg|right|400px|thumb|Figure 6. Schematic representation of a hydraulic jump propagating with velocity <math>c</math>. In the frame moving with velocity <math>c</math> the hydraulic jump appears stationary; time derivatives are zero. The corresponding mass and momentum balance equations from which the propagation characteristics can be derived are indicated in the figure. The symbols used stand for: <math>u</math>= flow velocity in a fixed frame, <math>v</math>= flow velocity in the moving frame, <math>D</math>= water depth, <math>g</math>=gravitational acceleration; subscripts 1 and 2 indicate upstream and downstream conditions, respectively.]]<br />
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<math>v_1=u_1 – c = - \Large \sqrt{ \frac{g D_2 (D_2 + D_1)}{2 D_1}} \normalsize , \quad \quad (1) </math> <br />
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<math>v_2=u_2 – c = - \Large \sqrt{ \frac{g D_1 (D_2 + D_1)}{2 D_2}} \normalsize , \quad \quad (2) </math> <br />
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where <math>c</math> is the bore celerity, <math>v</math> the velocity in the moving frame and <math>u</math> in the fixed frame. These equations show that the problem is entirely determined by the depth ratio <math>D_2 / D_1</math>, or equivalently by <math>\Delta D / D_1</math>, where <math>\Delta D = D_2 – D_1</math> is the bore height. The Froude numbers around the jump, in the moving frame can be obtained from equations (1) and (2):<br />
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<math>F_1^2 = \Large \frac{v_1^2}{g D_1}\normalsize = \large \frac{D_2 (D_1+D_2)}{2 D_1^2} \normalsize , \quad \quad (3) </math><br />
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<math>F_2^2 = \Large \frac{v_2^2}{g D_2}\normalsize = \large \frac{D_1 (D_2+D_1)}{2 D_2^2} \normalsize . \quad \quad (4)</math> <br />
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Knowing that <math>D_2 > D_1</math>, it is straightforward to see that <math>F_1 > 1</math> and <math>F_2 < 1</math>. The jump correspond to the passage from a supercritical flow (<math>F_1 > 1</math>) to a subcritical flow (<math>F_2 < 1</math>). The bore intensity is characterized equally by <math>\Delta D / D_1</math> or by the Froude number <math>F_1</math>.<br />
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If <math>F_2 = 1</math> (the bore height <math> \Delta D</math> is zero) the bore velocity <math> c </math> is equal to <br />
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<math>c_2 = u_2 + \sqrt{g D_2}</math>. <br />
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The inequality <math>F_2 < 1</math> therefore implies <math>c < c_2</math>. Because <math>c_2</math> is the propagation speed of long-wave disturbances upstream of the bore, these disturbances (undulations) will catch up to the bore. A slowly propagating bore (<math>F_2 << 1</math>) will thus grow faster and become higher than a fast propagating bore (<math>F_1, F_2 </math> close to 1) <ref>Dronkers, J.J. 1964. Tidal computations in rivers and coastal waters. North-Holland Publ. Co., 518 pp.</ref>. <br />
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It can be shown that conservation of mass and momentum at the transition does not imply conservation of energy. From the mass and momentum equations the following expression for the energy dissipation is obtained <ref name=L48>Lemoine, R. 1948. Sur les ondes positives de translation dans les canaux et sur le ressaut ondulé de faible amplitude. Houille Blanche: 183-185</ref> <ref> Stoker, J.J. 1957. Water Waves. Interscience, New York</ref>:<br />
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<math>Q \Delta E = D_1 V_1 [ \rho g \Delta D + 0.5 \rho (v_2^2 -v_1^2) ] = \Large \frac{\rho g}{4} \sqrt{\frac{g (D_1+D_2)}{2 D_1 D_2}}\normalsize (D_2 – D_1)^3 , \quad \quad (5)</math> <br />
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Two forms of energy dissipation can occur at the transition, leading to two different types of bores: undular and turbulent bores.<br />
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===Undular bores===<br />
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For <math>F_1</math> smaller than approximately 1.3, the bore transition is smooth and followed by a wave train (Fig. 1 right). The bore then consists of a mean jump between two water depths (see Fig. 6) on which secondary waves are superimposed. This type of bore is usually called an undular bore<ref name=C>Chanson, H. 2009. Current knowledge in hydraulic jumps and related phenomena. A survey of experimental results. European Journal of Mechanics-B/Fluids 28: 191-210</ref> and Favre (1935) <ref>Favre, H. 1935. Etude théorique et expérimentale des ondes de translation dans les canaux découverts (Theoretical and experimental study of travelling surges in open channels), Dunod, Paris</ref> was the first to describe this phenomenon from laboratory experiments. That is why undular bores are sometimes referred to as Favre waves. This phenomenon is a dispersive wave process (http://www.coastalwiki.org/wiki/Dispersion_(waves)), which is also named “dispersive shock” in the mathematical community.<br />
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[[Image:DispersiveBore.jpg|right|500px|thumb|Figure 7. Illustration of the two undular tidal bore regimes (Garonne River, Bonneton et al. 2015). Panels a, b: Dispersive regime (“mascaret” in French), F1=1.27. Panels c, d: Dispersive-like regime, Fr=1.08. Black line: elevation in the mid-channel; magenta line: elevation close to the river bank. Panel a:Two-dimensional (2-D) phase structure. Panel c: Quasi-1D phase structure.]]<br />
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A simple model describing the secondary waves attached to the bore was proposed by Lemoine (1948) <ref name=L48></ref>. He considered that secondary waves can be approximately described by linear theory. The propagation speed in the fixed frame is, according to linear [[shallow-water wave theory]],<br />
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<math> c_w = u_2 + \sqrt{gD_2 (1- \frac{k^2 D_2^2}{3})} , \quad \quad (6)</math><br />
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where <math>k=2 \pi / \lambda</math> is the wave number and <math>\lambda</math> the wavelength. The secondary waves are stationary in a frame moving with the bore front, i.e. <math>c_w = c</math>. This equality provides an estimate of the wavelength: <br />
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<math>\lambda=\sqrt{2/3} \pi D_2 (F_1 – 1)^{-1/2} . \quad \quad (7)</math><br />
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The secondary waves are stationary in the frame moving with the bore front, but in this frame wave energy is radiated behind the front. Equating the energy flux with the mean bore dissipation (Eq. 5) gives the secondary wave amplitude as a function of <math>F_1</math>:<br />
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<math>a_w=\frac{4}{3\sqrt{3}} D_2 (F_1 – 1) . \quad \quad (8)</math><br />
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As this approach ignores wave-induced mass transport it is valid only for very small bores (<math>F_1</math> close to 1)<ref>Wilkinson, M.L. and Banner, M.L. 1977. 6th Australasian Hydraulics and Fluid Mechanics Conf. Adelaide, Australia, 5-9 December 1977</ref>. Nevertheless, equations (7) and (8) appear to give a correct estimate of the observed wavelength and amplitude of undular bore propagating in rectangular channels <ref>Binnie, A. M., & Orkney, J. C. (1955). Experiments on the flow of water from a reservoir through an open horizontal channel II. The formation of hydraulic jumps. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 230(1181), 237-246</ref><ref>Chanson, H. (2010). Undular tidal bores: basic theory and free-surface characteristics. Journal of Hydraulic Engineering, 136(11), 940-944</ref>. <br />
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[[Image:DispersiveUndularBores.jpg|left|200px|thumb|Figure 8. Numerical simulations of the two undular tidal bore regimes. Panel a: Dispersive regime, F1=1.20. Panel b: Dispersive-like regime, F1=1.05. From Chassagne et al. 2019<ref name=CF></ref>.]]<br />
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In reality, natural estuary and river channels are non-rectangular and present most of the time a variable cross-section with an approximately trapezoidal shape and gently sloping banks. The propagation of undular bores over channels with variable cross-sections was studied by Treske (1994)<ref name=Tr>Treske, A. 1994. Undular bore (Favre-waves) in open channels - Experimental studies, J. Hydraulic Res. 32: 355-370</ref> in the laboratory and by Bonneton et al. (2015)<ref name=B15></ref> in the field. Both studies identified a transition around <math> F_t=1.15</math>. For <math>F_1 > F_t</math> the secondary wave field in the mid channel is very similar to the dispersive waves (Favre waves) described above, and follow the relations (7) and (8)<ref name=B15></ref>. For <math>F_1 < F_t</math>, the secondary wave wavelength in the whole channel is at least two to three times larger than in a rectangular channel for the same Froude numbers. It was shown that this new undular bore regime (Figs. 7 c,d and 8 b) differs significantly from classical dispersive undular bores in rectangular channels (i.e. Favre waves). Chassagne et al. (2019) <ref name=CF>Chassagne, R., Filippini, A., Ricchiuto, M. and Bonneton, P. 2019. Dispersive and dispersive-like bores in channels with sloping banks. Journal of Fluid Mechanics 870: 595-616. doi:10.1017/jfm.2019.287</ref> recently showed that this undular bore regime (named dispersive-like bore) is controlled by hydrostatic non-dispersive wave properties, with a dynamics similar to [[Infragravity waves|edge-waves]] in the near-shore. The transition between dispersive and dispersive-like bores is illustrated on Fig. 7 and 8. The dispersive-like bores are characterized by low wave steepness, which make them difficult to visually observe in the field. This is why such tidal bores are generally ignored and why tidal bore occurrence in the field is generally underestimated <ref> Bonneton, P., Van de Loock, J., Parisot, J-P., Bonneton, N., Sottolichio, A., Detandt, G., Castelle, B., Marieu, V. and Pochon, N. 2011. On the occurrence of tidal bores – The Garonne River case. Journal of Coastal Research, SI 64: 11462-1466</ref> <ref> Bonneton, N., Bonneton, P., Parisot, J-P., Sottolichio, A. and Detandt G. 2012. Tidal bore and Mascaret - example of Garonne and Seine Rivers. Comptes Rendus Geosciences, 344, 508-515</ref>. <br />
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===Breaking bores===<br />
For large Froude numbers, bores correspond to turbulent breaking fronts (Fig. 5), where the energy is dissipated by turbulent eddies<ref>Tu, J. and Fan, D. 2017. Flow and turbulence structure in a hypertidal estuary with the world's biggest tidal bore. Journal of Geophysical Research: Oceans, 122: 3417-3433</ref>. The transition between undular and turbulent bores is shown in Fig. 11. <br />
Before arrival of the tidal bore the current velocity is generally low and in the ebb direction. At the arrival of the bore front the current velocity is almost instantaneously reversed into the flood direction and reaches a high value within minutes. Fig. 9 shows the sharp increase in the current velocity and suspended sediment concentration recorded in the megatidal Baie du Mont Saint Michel at spring tide when the tidal flood wave enters the tidal flat area and the small rivers at the head of the Baie <ref name=Fu16> Furgerot, L., Mouazé, D., Tessier, B., Perez, L., Haquin, S., Weill, P., & Crave, A. (2016). Sediment transport induced by tidal bores. An estimation from suspended matter measurements in the Sée River (Mont-Saint-Michel Bay, northwestern France). Comptes Rendus Géoscience, 348(6), 432-441</ref>. The sudden strong change of the current velocity has an important stirring effect on the bed sediments, causing a sharp increase of the suspended sediment concentration. Turbulent bores contribute significantly to upstream sediment transport<ref>Reungoat, D., Lubin, P., Leng, X. and Chanson, H. 2018. Tidal bore hydrodynamics and sediment processes: 2010–2016 field observations in France. Coastal Engineering Journal 60: 484-498</ref>.<br />
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[[Image:TidalBoreSedimentSeeRiver_Furgerot.jpg|center|900px|thumb|Figure 9. Measurement of sediment transport by a tidal bore in the Sée River on 8 May 2012 (Furgerot et al, 2016 <ref name=Fu16></ref>). Panel 1: Tidal bore entering the Sée channel at the head of the Baie du Mont Saint Michel. The monastery is visible at the background. Panel 2: Map of the inner part of the Baie du Mont Saint Michel. The measuring location in the Sée River is indicated by the red star. Panel 3: Temporal variation of the vertical distribution of suspended sediment concentration (top), current velocity (middle) and sediment flux just (bottom) before and after arrival of the tidal bore. The current is ebb-directed with very low velocity just before arrival of the tidal bore and reverses to a flood-directed velocity simultaneously with the arrival of the tidal bore (middle panel). A very high short peak in the suspended sediment concentration near the bed occurs at the passage of the tidal bore front. High suspended sediment concentrations over the entire vertical (mainly fine silty sand) are recorded about 5 minutes later representing the sediment advected by the tidal bore (top panel). After a very high peak at the passage of the bore front the sediment flux is again high and in up-river direction some minutes later. The sediment flux is much lower during the remaining flood period (bottom panel) and similar to the up-river sediment flux when a tidal bore is absent. <br />
A video of the arrival of the tidal bore can be viewed by clicking [https://www.youtube.com/watch?v=waeS1MvhT9M here]. The photo of panel 1 is a still from the video.]]<br />
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In many tidal rivers the bore propagation near the shallow channel banks differs from the bore propagation in the deeper middle part of the channel. The local Froude number is relatively lower at the deeper parts of the channel, where the bore has often an undulating character, while a higher breaking bore occurs in the shallower parts. This phenomenon is illustrated in Fig. 10 for the tidal bore in the Petitcodiac and Kampar rivers. <br />
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[[Image:PetitcodiacRiver-KamparRiver.jpg|center|800px|thumb|Figure 10. Left image: Tidal bore in the Petitcodiac River, which is undular at the middle of the channel and breaking near the channel banks. Right image: Breaking tidal bore in the Kampar River, Sumatra.]]<br />
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==Modelling==<br />
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Tidal bore formation involves a large range of temporal and spatial scales, from the scale of the estuary to the turbulence scale. For this reason, it is difficult to integrate all these processes into a comprehensive model, either a physical model (laboratory experiments) or a numerical model. <br />
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===Physical models===<br />
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[[Image:FlumeUndularBores.jpg|left|400px|thumb|Figure 11. Experimental study of undular bores (Favre-waves) in open rectangular channels (Treske 1994<name=Tr></ref>). Undular bores, Fr=1.2 and 1.3; transition to a turbulent bore, Fr=1.35; turbulent bore, Fr=1.45.]]<br />
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Due to the large range of scales, it is impossible to design a laboratory experiment in close similitude with natural tidal bores. However, leaving aside the tidal wave transformation and bore formation, the bore in itself (i.e. hydraulic jump in translation) can be studied in detail from flume experiments. The bore is commonly generated in a rectangular flume by using a fast-closing gate at the upstream end of the flume<ref name=Tr></ref><ref name=C></ref>. This method allows the study of the different bore regimes (see Fig. 11) and provides valuable insights in secondary wave structure and vortical motions. <br />
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To avoid the abrupt bore generation of the above method, Rousseaux et al. (2016)<ref name=R></ref> proposed a novel approach. This method mimics the tidal asymmetry met in nature between the ebb and the flood. Fig. 12 shows an example of a tidal-like bore generated with this method.<br />
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[[Image:FlumeUndularBoresDye.jpg|center|700px|thumb|Figure 12. Experimental study of tidal-like bore using a laser sheet and fluorescent dye (Rousseaux et al. 2016<ref name=R></ref>).]]<br />
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===Numerical models===<br />
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[[Image:BreakingBoreLES.jpg|left|400px|thumb|Figure 13. Large Eddy Simulation of turbulence generated by a weak breaking bore. Streamlines indicate recirculation structures under the bore (Lubin et al. 2010<ref name=L></ref>).]]<br />
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Recent approaches, based on the resolution of the general Navier Stokes equations in their multiphase form (water phase and air phase), allow a detailed description of bore structure, turbulence and air entrainment in a roller at the bore front<ref name=L>Lubin, P., Chanson, H. and Glockner, S. 2010. Large eddy simulation of turbulence generated by a weak breaking tidal bore. Environmental Fluid Mechanics 10: 587-602</ref><ref>Berchet, A., Simon, B., Beaudoin, A., Lubin, P., Rousseaux, G. and Huberson, S. 2018. Flow fields and particle trajectories beneath a tidal bore: A numerical study. International Journal of Sediment Research 33: 351-370</ref>. Figure 13 presents the simulation of recirculating structures under a breaking bore. Navier-Stokes approaches are dedicated to small scale bore processes and cannot be applied to tidal bores at the estuarine scales because of limited computation power. Such applications would require long-wave models, where small scale vorticity motions are parametrized and not directly resolved.<br />
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[[Image:UndularBoreDevelopmentModel.jpg|right|500px|thumb|Figure 14. Serre-Green Naghdi simulation of an undular bore. Comparisons between experimental data (at 6 gauges, Fr=1.104) from Soares-Frazao and Zech (2002) <ref>Soares-Frazão S. and Zech Y. 2002. Undular bores and secondary waves - Experiments and hybrid finite-volume modeling. Journal of Hydraulic Research, International Association of Hydraulic Engineering and Research (IAHR) 40: 33-43</ref> and model prediction (Tissier et al. 2011<ref name=T></ref>). ]] <br />
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The most common long-wave model is the depth-averaged Saint Venant or Non Linear Shallow Water (NSW) model, which assumes hydrostatic pressure. This model gives a good description of the large-scale tidal wave transformation. The properties of breaking turbulent bores, are also quite well described by the non-dispersive NSW equations with jump conditions <ref>Chanson, H. 2012. Tidal bores, aegir, eagre, mascaret, pororoca: Theory and observations. World Scientific</ref>. <br />
However, the onset of a tidal bore and its evolution upstream is controlled by non-hydrostatic dispersive mechanisms<ref name=P></ref>. Although the onset of the tidal bore can be well described by classical weakly dispersive weakly nonlinear Boussinesq-type equations (<ref name=P>Peregrine, D. H. 1966. Calculations of the development of an undular bore. Journal of Fluid Mechanics 25: 321-330</ref>, see [https://en.wikipedia.org/wiki/Boussinesq_approximation_(water_waves) Boussinesq equations]), the subsequent nonlinear evolution, for high-intensity tidal bores, requires the use of the basic fully nonlinear Boussinesq equations, named Serre-Green Naghdi (SGN) equations<ref name=B11c>Bonneton, P., Barthélemy, E., Chazel, F., Cienfuegos, R., Lannes, D., Marche, F. and Tissier, M. 2011. Recent advances in Serre–Green Naghdi modelling for wave transformation, breaking and runup processes. European Journal of Mechanics-B/Fluids 30: 589-597</ref><ref name=T>Tissier, M., Bonneton, P., Marche, F., Chazel, F., & Lannes, D. 2011. Nearshore dynamics of tsunami-like undular bores using a fully nonlinear Boussinesq model. Journal of Coastal Research SI 84: 603-607</ref><ref name=F></ref>. This modelling approach allows an accurate description of both the tidal bore formation on the estuarine scale (Fig. 4) and the bore structure on the local scale (Fig. 14).<br />
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==See also==<br />
: [[Tidal asymmetry and tidal basin morphodynamics]]<br />
: [[Ocean and shelf tides]]<br />
: [[Morphology of estuaries]]<br />
: [[Estuaries]]<br />
: [[Dam break flow]]<br />
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==References==<br />
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<references/><br />
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{{2Authors<br />
|AuthorID1=15152<br />
|AuthorFullName1= Philippe Bonneton <br />
|AuthorName1= Bonneton P<br />
|AuthorID2=120<br />
|AuthorFullName2=Job Dronkers<br />
|AuthorName2=Dronkers J<br />
}}<br />
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[[Category:Physical coastal and marine processes]]<br />
[[Category:Estuaries and tidal rivers]]<br />
[[Category:Hydrodynamics]]</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Dam_break_flow&diff=76332Dam break flow2020-01-15T20:14:43Z<p>Dronkers J: Created page with " This article discusses the often catastrophic flows that result from the failure of high dams that protect low-lying land. Dam break mechanisms are not dealt with; for this t..."</p>
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<div><br />
This article discusses the often catastrophic flows that result from the failure of high dams that protect low-lying land. Dam break mechanisms are not dealt with; for this the reader is referred to the extensive literature existing on this subject, see for example Zhang et al. (2016) <ref>Zhang, L., Peng, M., Chang, D. and Xu, Y. 2016. Dam failure and Risk Assessment. John Wiley and Sons, Singapore</ref> and Almog et al. (2011) <ref>Almog, E., Kelham, P and King, R. 2011. Modes of dam failure and monitoring and measuring techniques. Environmental Agency,UK https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/290819/scho0811buaw-e-e.pdf</ref>.<br />
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==Introduction==<br />
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[[image:Dijkdoorbraak1953.png|thumb|left|300px|Fig. 1. Sea dikes protecting low-lying polders in the Netherlands were breached during the extreme storm surge of 31 January 1953.]] <br />
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Dam failure can lead to disastrous situations. Most dam break tragedies are related to the collapse of reservoir dams in mountain rivers. The failure of sea dikes can also cause major disasters, although in this case the level difference is not as large. A dramatic example is the failure of more than fifty sea dikes in the Netherlands during the extreme storm surge of 1953, see figure 1. Many of these dikes protected land lying below the average sea level, while the storm surge level exceeded more than five meters. Rapid flooding killed more than two thousand people who were unable to flee in time to safe places. The most common dam failure mechanisms are related to overtopping and seepage (also called piping or internal erosion)<ref name=F8>Froehlich, D.C. 2008. Embankment Dam Breach Parameters and Their Uncertainties. Journal of Hydraulic Engineering, ASCE 134: 1708-1721</ref>. In the case of the 1953 storm surge, overtopping and subsequent scour of the interior dike slope was the most important dike failure mechanism. <br />
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[[image:DamBreakFlowPrinciple.jpg|thumb|center|600px|Fig. 2. Left panel: Schematic representation of water retention behind a dam. Right panel: Positive downstream and negative upstream surges following instantaneous dam removal.]]<br />
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The consequences of dam failure have been studied for more than a century. It nevertheless remains a challenging topic due to the high non-linearity of the flood wave propagation. The problem can be tackled with numerical models, but rough estimates and insight into the tidal wave dynamics can be obtained with analytical solution methods.<br />
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==Frictionless dam-break flow: analytical solution==<br />
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Analytical solutions relate to idealized situations as depicted in Fig. 2. The initial situation consists of an infinite reservoir with a water level that is <math> h_0 </math> higher than the horizontal ground level downstream of the dam. Dam break is simulated by instantaneous removal of the dam. This causes a positive surge in the positive <math> x </math>-direction and a negative surge in the negative <math> x </math>-direction. The floor is dry in front of the positive surge and the body of water behind the negative surge is undisturbed: water level =<math> h_0 </math> and current speed <math> u = 0 </math>.<br />
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[[image:SouthForkDamFailure1889.jpg|thumb|left|300px|Fig. 3. The earth-filled South Fork Dam on Lake Conemaugh (Pennsylvania, US) collapsed in 1889, killing 2,209 people in downstream villages.]]<br />
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The study of the dam break-flow was triggered by several dam failures in the 19th century, in particular the breach of the South Fork Dam in Pennsylvania (USA) in 1889, Fig. 3. Three years later Ritter <ref> Ritter, A. 1892. Die Fortpflanzung der Wasserwellen. Zeitschrift des Vereines Deutscher Ingenieure 36: 947-954 </ref> published an exact analytical solution for dam-break flow by assuming that frictional effects can be ignored. The derivation is given in box 1. According to this solution, the tip of the positive surge advances at high speed (supercritical flow) given by <math> u_f = 2 c_0</math>, where <math>c_0 = \sqrt {gh_0}</math> and <math> g </math> is the gravitational acceleration. The shape of the positive and negative wave is a concave-up parabola,<br />
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<math>h(x,t)= h_0, \; x<-c_0 t; \quad h(x,t)= \Large\frac{h_0}{9}\normalsize \; (2 - \Large\frac{x}{c_0 t}\normalsize)^2 , \, -c_0 t<x<2c_0 t; \quad h(x,t)= 0, \, x>2c_0 t , \qquad (1)</math><br />
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see Fig. 4. According to Eq. (1) and Box 1, the discharge through the breach per unit width is given by<br />
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<math>q = \frac{8}{27} h_0 \sqrt{g h_0}. \qquad (2) </math> <br />
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Figure 4 also shows the shape of the dam break wave that was observed in laboratory experiments. For small values of <math> x / t </math>, the frictionless solution corresponds fairly well with the observations. However, the front zone is different: the shape is a bull nose, rather than a sharp edge. The front also advances more slowly; the speed of the front decreases with time and is closer to <math> u_f = c_0 </math> than to <math> u_f = 2 c_0 </math>. The reason for this difference is the neglect of frictional effects that are important in the thin fluid layer near the front.<br />
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[[image:DamBreakFlowDerivation.png|thumb|center|900px|Box 1. Derivation of the solution for frictionless dam break flow.]]<br />
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==Dam-break flow with friction==<br />
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[[image:DamBreakWaveProfiles.jpg|thumb|left|400px|Fig. 4. Wave profile after dam break. The red curve corresponds to the frictionless solution Eq. 1. The blue band represents data from different laboratory experiments performed at times <math>\small t \sim (40-80) \, \sqrt {h_0 / g}\normalsize </math> after removal of the dam <ref>Dressler, R. 1954. Comparison of theories and experiments for the hydraulic dam-break wave. Proc. Int. Assoc. Scientific Hydrology Assemblée Générale, Rome, Italy 3 (38)M 319–328</ref> <ref>Schoklitsch, A. 1917. Über Dambruchwellen. Kaiserliche Akademie der Wissenschaften, Wien, Mathematisch-Naturwissenschaftliche Klasse, Sitzungberichte IIa, 126: 1489–1514</ref><ref>Cavaillé,Y. 1965. Contribution à l’étude de l’écoulement variable accompagnant la vidange brusque d’une retenue. Publ. Scient. et Techn. du Ministère de l’Air, 410, Paris, France, 165</ref>. The frictionless solution only depends on <math>x/t</math>. Observed wave profiles also depend on time <math>t</math> because of the decreasing wave tip speed.]]<br />
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When friction terms are included in the flow equations, there is no exact analytical solution. It is generally assumed that the frictionless flow equations are approximately valid in a short period after dam break and for small values of <math>x / (c_0 t) </math>. In the front zone, where the water depth is small, the momentum balance is dominated by frictional momentum dissipation. If the inertia terms <math>\partial u / \partial t + u \partial u / \partial x </math> in the momentum equation are ignored, then the current in the front region is mainly determined by the balance of gravitational acceleration <math> g \partial h / \partial x </math> and shear stress <math>\tau</math>, the latter term being proportional to the square of the flow velocity<ref>Dressler, R.F. 1952. Hydraulic resistance effect upon the dambreak functions. J. Res. Natl. Bureau of Standards, 49(3): 217–225</ref><ref>Whitham, G.B. 1955. The effects of hydraulic resistance in the dam-break problem. Proc. Roy. Soc. of London, Serie A, 227: 399–407</ref><ref>Hogg, A.J. and Pritchard, D. 2004. The effects of hydraulic resistance on dam-break and other shallow inertial flows. J. Fluid Mech. 501: 179–212</ref><ref name=C09>Chanson, H. 2009. Application of the method of characteristics to the dam break wave problem. Journal of Hydraulic Research 47: 41–49</ref>. With such models the shape of the wave front is given by <math>h(s) \propto s^n, \; n=1/2</math>, where <math>s</math> is the distance measured from the wave front. The wave front speed <math>u_f</math> decreases with time. At large times <math>t>>t_{\infty}</math>, the wave front speed varies approximately as <math>u_f \approx c_0 \sqrt{t_{\infty}/t}</math> <ref name=C09></ref>. Here, <math>t_{\infty} = \sqrt{h_0/g}/(3 c_D)</math> and <math>c_D</math> is the friction coefficient (value in the range <math>\approx (1-5)\, 10^{-3}</math>). A more elaborate model of the frictional boundary layer near the wave front was studied by Nielsen (2018) <ref name=PN>Nielsen, P. 2018 Bed shear stress, surface shape and velocity field near the tips of dam-breaks, tsunami and wave runup velocity. Coastal Engineering 138: 126–131</ref>. According to this model, the wavefront is even more blunt, corresponding to <math> n = 1/4 </math>, which agrees well with laboratory experiments. This model also reveals a strong downward velocity component at the wavefront, which can contribute to the dislodging of particles from the sediment bed <ref name = PN> </ref>. This may explain the high near-bed of suspended concentrations associated with propagating surges observed in the field<ref>Khezri, N. and Chanson, H. 2012. Inception of bed load motion beneath a bore. Geomorphology 153: 39–47</ref>, see also the article [[Tidal bore dynamics]]. <br />
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Data from numerous reservoir dam breaks that have occurred in the past have provided empirical formulas for the maximum discharge <math>Q_{max}</math> through the breach <ref>Froehlich, D.C. 2016. Predicting Peak Discharge from Gradually Breached Embankment Dam. Journal of Hydraulic Engineering, ASCE 04016041</ref><ref name=W> Wang, B., Chen, Y., Wu, C., Peng, Y., Song, J., Liu, W. and Liu, X. 2018. Empirical and semi-analytical models for predicting peak outflows caused by embankment dam failures. Journal of Hydrology 562: 692–702</ref>. From this data it was deduced that the width of the breach is mainly related to the volume of water <math>V</math> in the reservoir (volume above breach level). A reasonable estimate of the width is given by <ref name=F8></ref> <math> B \approx 0.3 V ^ {1/3} </math>. Empirical formulas for the maximum dam break discharge then yield <ref>Webby, M. G. 1996. Discussion of ‘Peak outflow from breached embankment dam.’ by D. C. Froehlich. J. Water Resour. Plann. Management 122:4(316), 316–317</ref> <ref name=W></ref><br />
<br />
<math>Q_{max} \approx 0.04 \sqrt{g} \, V^{0.37} h_0^{1.4} \approx 0.15 h_0 \, B \, \sqrt{g h_0} \, V^{0.04} h_0^{-0.1} , \qquad (3)</math> <br />
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or<br />
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<math> q_{max} \approx 0.22 h_0 \, \sqrt{g h_0} , \qquad (4)</math><br />
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where in the approximation for the maximum discharge per unit width we have considered a large reservoir volume (<math>V \approx 10^7 m^3</math>) and a water depth <math>h_0 \approx 15 m</math>. The empirical estimate (4) is about 75% of the estimate (2) given by the frictionless flow solution.<br />
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<br />
==Numerical models==<br />
<br />
The analytical methods for describing dam-break flow provide a qualitative picture and some first-order estimates for the wave profile and wave speed. They may only be used in situations that can be represented schematically by a simple prismatic channel. In most actual field situations, the dam-break flow must be modeled numerically. Detailed simulation of the forward and backward wave fronts requires 3D models of the Boussinesq type, taking into account vertical fluid accelerations<ref>Castro-Orgaz, O. and Chanson, H. 2017. Ritter’s dry-bed dam-break flows: positive and negative wave dynamics. Environ Fluid Mech (2017) 17:665–694</ref>. To correctly model the strong temporal and spatial gradients of the surging wave, a fine computational grid is required, with resulting long computer times. See also [[Tidal bore dynamics]]. <br />
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==References==<br />
<references/><br />
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{{author<br />
|AuthorID=120<br />
|AuthorFullName=Job Dronkers<br />
|AuthorName=Dronkers J}}<br />
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[[Category:Physical coastal and marine processes]]<br />
[[Category:Hydrodynamics]]</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Testpage1&diff=76331Testpage12020-01-15T20:13:23Z<p>Dronkers J: </p>
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<div>=Dam break flow=<br />
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This article discusses the often catastrophic flows that result from the failure of high dams that protect low-lying land. Dam break mechanisms are not dealt with; for this the reader is referred to the extensive literature existing on this subject, see for example Zhang et al. (2016) <ref>Zhang, L., Peng, M., Chang, D. and Xu, Y. 2016. Dam failure and Risk Assessment. John Wiley and Sons, Singapore</ref> and Almog et al. (2011) <ref>Almog, E., Kelham, P and King, R. 2011. Modes of dam failure and monitoring and measuring techniques. Environmental Agency,UK https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/290819/scho0811buaw-e-e.pdf</ref>.<br />
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==Introduction==<br />
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[[image:Dijkdoorbraak1953.png|thumb|left|300px|Fig. 1. Sea dikes protecting low-lying polders in the Netherlands were breached during the extreme storm surge of 31 January 1953.]] <br />
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Dam failure can lead to disastrous situations. Most dam break tragedies are related to the collapse of reservoir dams in mountain rivers. The failure of sea dikes can also cause major disasters, although in this case the level difference is not as large. A dramatic example is the failure of more than fifty sea dikes in the Netherlands during the extreme storm surge of 1953, see figure 1. Many of these dikes protected land lying below the average sea level, while the storm surge level exceeded more than five meters. Rapid flooding killed more than two thousand people who were unable to flee in time to safe places. The most common dam failure mechanisms are related to overtopping and seepage (also called piping or internal erosion)<ref name=F8>Froehlich, D.C. 2008. Embankment Dam Breach Parameters and Their Uncertainties. Journal of Hydraulic Engineering, ASCE 134: 1708-1721</ref>. In the case of the 1953 storm surge, overtopping and subsequent scour of the interior dike slope was the most important dike failure mechanism. <br />
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[[image:DamBreakFlowPrinciple.jpg|thumb|center|600px|Fig. 2. Left panel: Schematic representation of water retention behind a dam. Right panel: Positive downstream and negative upstream surges following instantaneous dam removal.]]<br />
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The consequences of dam failure have been studied for more than a century. It nevertheless remains a challenging topic due to the high non-linearity of the flood wave propagation. The problem can be tackled with numerical models, but rough estimates and insight into the tidal wave dynamics can be obtained with analytical solution methods.<br />
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==Frictionless dam-break flow: analytical solution==<br />
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Analytical solutions relate to idealized situations as depicted in Fig. 2. The initial situation consists of an infinite reservoir with a water level that is <math> h_0 </math> higher than the horizontal ground level downstream of the dam. Dam break is simulated by instantaneous removal of the dam. This causes a positive surge in the positive <math> x </math>-direction and a negative surge in the negative <math> x </math>-direction. The floor is dry in front of the positive surge and the body of water behind the negative surge is undisturbed: water level =<math> h_0 </math> and current speed <math> u = 0 </math>.<br />
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[[image:SouthForkDamFailure1889.jpg|thumb|left|300px|Fig. 3. The earth-filled South Fork Dam on Lake Conemaugh (Pennsylvania, US) collapsed in 1889, killing 2,209 people in downstream villages.]]<br />
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The study of the dam break-flow was triggered by several dam failures in the 19th century, in particular the breach of the South Fork Dam in Pennsylvania (USA) in 1889, Fig. 3. Three years later Ritter <ref> Ritter, A. 1892. Die Fortpflanzung der Wasserwellen. Zeitschrift des Vereines Deutscher Ingenieure 36: 947-954 </ref> published an exact analytical solution for dam-break flow by assuming that frictional effects can be ignored. The derivation is given in box 1. According to this solution, the tip of the positive surge advances at high speed (supercritical flow) given by <math> u_f = 2 c_0</math>, where <math>c_0 = \sqrt {gh_0}</math> and <math> g </math> is the gravitational acceleration. The shape of the positive and negative wave is a concave-up parabola,<br />
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<math>h(x,t)= h_0, \; x<-c_0 t; \quad h(x,t)= \Large\frac{h_0}{9}\normalsize \; (2 - \Large\frac{x}{c_0 t}\normalsize)^2 , \, -c_0 t<x<2c_0 t; \quad h(x,t)= 0, \, x>2c_0 t , \qquad (1)</math><br />
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see Fig. 4. According to Eq. (1) and Box 1, the discharge through the breach per unit width is given by<br />
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<math>q = \frac{8}{27} h_0 \sqrt{g h_0}. \qquad (2) </math> <br />
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Figure 4 also shows the shape of the dam break wave that was observed in laboratory experiments. For small values of <math> x / t </math>, the frictionless solution corresponds fairly well with the observations. However, the front zone is different: the shape is a bull nose, rather than a sharp edge. The front also advances more slowly; the speed of the front decreases with time and is closer to <math> u_f = c_0 </math> than to <math> u_f = 2 c_0 </math>. The reason for this difference is the neglect of frictional effects that are important in the thin fluid layer near the front.<br />
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[[image:DamBreakFlowDerivation.png|thumb|center|900px|Box 1. Derivation of the solution for frictionless dam break flow.]]<br />
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==Dam-break flow with friction==<br />
<br />
[[image:DamBreakWaveProfiles.jpg|thumb|left|400px|Fig. 4. Wave profile after dam break. The red curve corresponds to the frictionless solution Eq. 1. The blue band represents data from different laboratory experiments performed at times <math>\small t \sim (40-80) \, \sqrt {h_0 / g}\normalsize </math> after removal of the dam <ref>Dressler, R. 1954. Comparison of theories and experiments for the hydraulic dam-break wave. Proc. Int. Assoc. Scientific Hydrology Assemblée Générale, Rome, Italy 3 (38)M 319–328</ref> <ref>Schoklitsch, A. 1917. Über Dambruchwellen. Kaiserliche Akademie der Wissenschaften, Wien, Mathematisch-Naturwissenschaftliche Klasse, Sitzungberichte IIa, 126: 1489–1514</ref><ref>Cavaillé,Y. 1965. Contribution à l’étude de l’écoulement variable accompagnant la vidange brusque d’une retenue. Publ. Scient. et Techn. du Ministère de l’Air, 410, Paris, France, 165</ref>. The frictionless solution only depends on <math>x/t</math>. Observed wave profiles also depend on time <math>t</math> because of the decreasing wave tip speed.]]<br />
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<br />
When friction terms are included in the flow equations, there is no exact analytical solution. It is generally assumed that the frictionless flow equations are approximately valid in a short period after dam break and for small values of <math>x / (c_0 t) </math>. In the front zone, where the water depth is small, the momentum balance is dominated by frictional momentum dissipation. If the inertia terms <math>\partial u / \partial t + u \partial u / \partial x </math> in the momentum equation are ignored, then the current in the front region is mainly determined by the balance of gravitational acceleration <math> g \partial h / \partial x </math> and shear stress <math>\tau</math>, the latter term being proportional to the square of the flow velocity<ref>Dressler, R.F. 1952. Hydraulic resistance effect upon the dambreak functions. J. Res. Natl. Bureau of Standards, 49(3): 217–225</ref><ref>Whitham, G.B. 1955. The effects of hydraulic resistance in the dam-break problem. Proc. Roy. Soc. of London, Serie A, 227: 399–407</ref><ref>Hogg, A.J. and Pritchard, D. 2004. The effects of hydraulic resistance on dam-break and other shallow inertial flows. J. Fluid Mech. 501: 179–212</ref><ref name=C09>Chanson, H. 2009. Application of the method of characteristics to the dam break wave problem. Journal of Hydraulic Research 47: 41–49</ref>. With such models the shape of the wave front is given by <math>h(s) \propto s^n, \; n=1/2</math>, where <math>s</math> is the distance measured from the wave front. The wave front speed <math>u_f</math> decreases with time. At large times <math>t>>t_{\infty}</math>, the wave front speed varies approximately as <math>u_f \approx c_0 \sqrt{t_{\infty}/t}</math> <ref name=C09></ref>. Here, <math>t_{\infty} = \sqrt{h_0/g}/(3 c_D)</math> and <math>c_D</math> is the friction coefficient (value in the range <math>\approx (1-5)\, 10^{-3}</math>). A more elaborate model of the frictional boundary layer near the wave front was studied by Nielsen (2018) <ref name=PN>Nielsen, P. 2018 Bed shear stress, surface shape and velocity field near the tips of dam-breaks, tsunami and wave runup velocity. Coastal Engineering 138: 126–131</ref>. According to this model, the wavefront is even more blunt, corresponding to <math> n = 1/4 </math>, which agrees well with laboratory experiments. This model also reveals a strong downward velocity component at the wavefront, which can contribute to the dislodging of particles from the sediment bed <ref name = PN> </ref>. This may explain the high near-bed of suspended concentrations associated with propagating surges observed in the field<ref>Khezri, N. and Chanson, H. 2012. Inception of bed load motion beneath a bore. Geomorphology 153: 39–47</ref>, see also the article [[Tidal bore dynamics]]. <br />
<br />
<br />
Data from numerous reservoir dam breaks that have occurred in the past have provided empirical formulas for the maximum discharge <math>Q_{max}</math> through the breach <ref>Froehlich, D.C. 2016. Predicting Peak Discharge from Gradually Breached Embankment Dam. Journal of Hydraulic Engineering, ASCE 04016041</ref><ref name=W> Wang, B., Chen, Y., Wu, C., Peng, Y., Song, J., Liu, W. and Liu, X. 2018. Empirical and semi-analytical models for predicting peak outflows caused by embankment dam failures. Journal of Hydrology 562: 692–702</ref>. From this data it was deduced that the width of the breach is mainly related to the volume of water <math>V</math> in the reservoir (volume above breach level). A reasonable estimate of the width is given by <ref name=F8></ref> <math> B \approx 0.3 V ^ {1/3} </math>. Empirical formulas for the maximum dam break discharge then yield <ref>Webby, M. G. 1996. Discussion of ‘Peak outflow from breached embankment dam.’ by D. C. Froehlich. J. Water Resour. Plann. Management 122:4(316), 316–317</ref> <ref name=W></ref><br />
<br />
<math>Q_{max} \approx 0.04 \sqrt{g} \, V^{0.37} h_0^{1.4} \approx 0.15 h_0 \, B \, \sqrt{g h_0} \, V^{0.04} h_0^{-0.1} , \qquad (3)</math> <br />
<br />
or<br />
<br />
<math> q_{max} \approx 0.22 h_0 \, \sqrt{g h_0} , \qquad (4)</math><br />
<br />
where in the approximation for the maximum discharge per unit width we have considered a large reservoir volume (<math>V \approx 10^7 m^3</math>) and a water depth <math>h_0 \approx 15 m</math>. The empirical estimate (4) is about 75% of the estimate (2) given by the frictionless flow solution.<br />
<br />
<br />
==Numerical models==<br />
<br />
The analytical methods for describing dam-break flow provide a qualitative picture and some first-order estimates for the wave profile and wave speed. They may only be used in situations that can be represented schematically by a simple prismatic channel. In most actual field situations, the dam-break flow must be modeled numerically. Detailed simulation of the forward and backward wave fronts requires 3D models of the Boussinesq type, taking into account vertical fluid accelerations<ref>Castro-Orgaz, O. and Chanson, H. 2017. Ritter’s dry-bed dam-break flows: positive and negative wave dynamics. Environ Fluid Mech (2017) 17:665–694</ref>. To correctly model the strong temporal and spatial gradients of the surging wave, a fine computational grid is required, with resulting long computer times. See also [[Tidal bore dynamics]]. <br />
<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
<br />
[[Category:Physical coastal and marine processes]]<br />
[[Category:Hydrodynamics]]</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Testpage2&diff=76330Testpage22020-01-14T21:16:18Z<p>Dronkers J: </p>
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<div>Tsunami<br />
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{{Definition|title=Tsunami <br />
|definition= Series of long waves caused by a strong local disturbance of the water mass. The wavelength is typically much larger than the wavelength of wind-generated waves and much smaller than the wavelength of tidal waves. }}<br />
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==Tsunami causes and occurrence==<br />
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[[Image:RingofFireUSGS.jpg|thumb|300px|left|Figure 1: Ring of fire around the Pacific. Image USGS.]]<br />
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The occurrence of a tsunami can have several causes<ref name=RV>Röbke, R.B. and Vött, A. 2017. The tsunami phenomenon. Progress in Oceanography 159: 296–322</ref>. The main cause, responsible for the strongest tsunamis, are seaquakes (submarine earthquakes): the sudden uplift of the seabed due to shifting earth plates. This mainly occurs in subduction zones, where an earth plate slides under an adjacent earth plate causing vertical motion of the submarine crust along the subduction line. The most important subduction zones lie along the edges of the Pacific Ocean, the so-called ring of fire (see Fig. 1). The strength of the tsunami depends not only on the vertical and horizontal size of the seafloor uplift, but also on the speed at which the seafloor rises. The strongest response occurs when this speed is comparable to the local wave propagation speed. The tsunami wave radiates in both directions perpendicular to the subduction line. <br />
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A second important cause is submarine gravity mass wasting. Such slides can be triggered by seismic activity at a sloping seabed (e.g., the shelf break) that is covered with a thick layer of unconsolidated material. The tsunami wave propagates in the direction of the slide and is strongest if the speed of the debris flow is comparable to local wave propagation speed. Gas formation (methane) due to the anaerobic degradation of organic material can contribute to the loss of stability of the sediment layer on the sloping seabed <ref>Tinivella, U., Accaino, F. and della Vedova, B. 2008. Gas hydrates and active mud volcanism on the south Shetland continental margin, Antarctic Peninsula. Geo-Mar. Lett. 28: 97–106</ref>.<br />
Volcanic activity and subaerial landslides can also cause tsunamis, but these are usually not as strong. A tsunami can in rare cases result from the impact of a large meteorite.<br />
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Another type of tsunamis, so-called meteotsunamis, can arise from atmospheric disturbances. Sudden local pressure fluctuations can generate a small setup or set-down of the water level that is amplified if the atmospheric front propagates at a speed comparable to the wave propagation speed or if the spatial/temporal scales coincide <ref>Monserrat, S., Vilibić, I. and Rabinovich, A.B. 2006. Meteotsunamis: atmospherically induced destructive ocean waves in the tsunami frequency band. Nat. Hazards Earth Syst. Sci. 6: 1035–1051</ref>. The amplitude of meteotsunamis is usually small, but it can increase strongly due to resonance effects in semi-closed basins (e.g., harbor seiches, which are damaging for moored ships).<br />
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==Tsunami characteristics==<br />
A tsunami usually consists of a number of waves (up to about ten) of different amplitude <ref>Grilli, S.T., Harris, J.C., Tajalli Bakhsh, T.S., Masterlark, T.L., Kyriakopoulos, C., Kirby, J.T. and Shi, F. 2013. Numerical simulation of the 2011 Tohoku tsunami based on a new transient FEM Co-seismic source: comparison to far- and near-field observations. Pure Appl. Geophys. 170: 1333–1359</ref>. The third, fourth or fifth wave are often the highest <ref> Murty, T.S. 1977. Seismic sea waves. Tsunamis. In: Stevenson, J.C. (Ed.), Bulletin of the Fisheries Research Board of Canada, vol. 198</ref>. The characteristic wave period is different for each tsunami, but usually much greater than the period of wind-driven waves (i.e., more than a few minutes) and much smaller than the tidal period (i.e., less than two hours). The wave height can be a few meters at the place of origin, but when the tsunami starts propagating over the ocean the wave height quickly becomes smaller and is then usually less than one meter<ref> Bolt, B.A., Horn, W.L., Macdonald, G.A. and Scott, R.F. 1975. Geological hazards. Earthquakes—Tsunamis—Volcanoes—Avalanches—Landslides—Floods. Springer, New York</ref>. The wavelength is much greater than the water depth and the energy loss during ocean propagation is small (approximately inversely proportional to the wavelength). The propagation speed <math>c</math> can therefore be approximated with the formula <math>c = \sqrt {gD}</math>, where <math>D</math> is the average depth and <math> g </math> the gravitational acceleration. Tsunamis travel at great speed across the ocean (<math>c</math> in the order of a few hundred m/s) covering distances of many thousands of kilometers without great energy loss.<br />
The energy flux <math> F </math> can be estimated with the formula <math>F = cE \approx (1/8) \rho g H ^ 2 \sqrt {gD}</math>, where <math>E</math> is the tsunami wave energy, <math> H </math> the tsunami wave height and <math>\rho</math> the water density. When the tsunami reaches the coastal zone, the water depth decreases sharply as does the propagation speed <math> c </math>. However, frictional energy dissipation being relatively modest, the energy flux <math>F</math> remains almost the same. This implies <math>H_{shore}/H_{ocean} \approx (D_{ocean}/D_{shore})^{1/4}</math>: the wave height <math>H</math> of the tsunami is strongly increased, up to about 5 times the wave height on the ocean. The wave height can be amplified even more in marine inlets, such as bays, fjords or harbours, where the tsunami energy flux is concentrated and accelerated due to strong funnel effects <ref name=RV></ref>. The tsunami waves are also distorted when entering shallow water; when the rear of the wave train is still traveling in deeper water it gets closer to the front of the wave train which is already travelling in shallow water. Differences in propagation speed of wave crest and wave trough contribute to steepening of the wave front on wide continental shelfs - wide compared to the tsunami wavelength.<br />
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When the tsunami wave arrives at the coast it runs up the shoreface (schematically depicted in Fig. 6). If the slope is steep (the width of the shoreface being much smaller than the wavelength of the tsunami, i.e. less than 10 km), the tsunami 'feels' the shoreface as a straight wall. The tsunami is then almost completely reflected and the wave height is doubled. The tsunami floods the coast as a surging wave with a relatively low speed that can be outrun. The wave run-up is not much higher than the wave height on the foreshore.<br />
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[[Image:Tsunami Phuket 2004.png|thumb|400px|left|Figure 2: The Indian Ocean tsunami of December 26, 2004, invading the coast at Phuket Thailand as a breaking bore. Picture from a camera lost on the beach. Image Flickr creative commons.]]<br />
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If the shoreface slope is gentle (the length of the foreshore being of the same order or greater than the wavelength), the tsunami transforms into an undular bore, with short waves riding on the main tsunami wave. When reaching the shore, the tsunami transforms further into a breaking bore (a wall of water, see Fig. 2) that propagates at great speed with a very fast rising water level. The wave run-up is much higher than the wave height at the toe of the shoreface (a factor of 2 and possibly more).<br />
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The above qualitative description suggests that the character of a tsunami is related to the surf similarity parameter <math>\xi</math> <ref name=MG> McGovern, D.J., Robinson, T., Chandler, I.D., Allsop, W. and Rossetto, T. 2018. Pneumatic long-wave generation of tsunami-length waveforms and their runup Coastal Engineering 138: 80–97</ref><ref name=LF>Larsen, B.E. and Fuhrman, D.R. 2019. Full-scale CFD simulation of tsunamis. Part 1: Model validation and run-up Coastal Engineering 151: 22–41</ref><ref name=MS>Madsen, P.A. and Schäffer, H.A. 2010. Analytical solutions for tsunami runup on a plane beach. J. Fluid Mech. 645: 27–57</ref>,<br />
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<math>\xi = \Large\frac{S}{\sqrt{2 A_0/L_{\infty}}}\normalsize = \Large\frac{S}{\omega} \sqrt{\frac{\pi g}{A_0}}\normalsize , </math><br />
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where <math>A_0</math> is the tsunami wave height above mean sea level at the toe of the shoreface slope, <math>L_{\infty} = g T^2/(2 \pi)</math> is the tsunami wave length at infinite depth, <math>S</math> is the shoreface slope and <math>\omega</math> is the tsunami wave period. Surging waves correspond to high values of <math>\xi</math> and breaking waves to low values. <br />
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[[Image:BandAcehTsunamiLeadingDepression.jpg|thumb|300px|left|Figure 3: Retreating shoreline before arrival of the major wave of the Indian Ocean tsunami at Banda Aceh on December 26, 2004. Image C.E. Synolakis <ref name=SB>Synolakis, C.E. and Bernard, E.N. 2006. Tsunami science before and beyond Boxing Day 2004. Phil. Trans. R. Soc. A. 364: 2231–2265</ref>.]]<br />
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A distinction is often made between two types of tsunamis: tsunamis where the largest wave crest precedes the largest wave trough (sometimes called leading-elevation N-wave or LEN-wave) and tsunamis where the largest wave crest is preceded by the largest wave trough (sometimes called leading-depression N-wave or LDN-wave). Both types of tsunami occur in practice. In case of a LDN-wave, the sea retreats over a large distance and part of the shoreface falls dry before arrival of the wave crest, see Fig. 3. This is an important signal for bathers that a high tsunami wave is approaching. A LDN-wave approaches the shore at a lower speed than a similar LEN-wave, but the runup speed on land is in both cases of the same order. <br />
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<br />
==Tsunami impact==<br />
Tsunamis can cause enormous damage to coastal infrastructure, crushing houses, deracinating trees and making many casualties, see Fig. 4. From historical records it has been estimated that more than a million people have been killed worldwide by tsunamis <ref>National Geophysical Data Center/World Data Service, 2015. Global historical tsunami database. Tsunami event data. <http://www.ngdc.noaa.gov/hazard/tsu_db.shtml></ref>. In low-lying coastal areas (less than 10 m elevation above mean sea level) tsunamis can penetrate several kilometers inland. There are even records of tsunamis that have penetrated several tens of kilometers inland and have reached levels of several tens of meters. The flood water volume is approximately equal to the water volume above beach level of the incident tsunami wave <ref>Bryant, E.A., 2008. Tsunami: The Underrated Hazard, second ed. Springer, Berlin</ref>. Runup velocities of strong tsunamis are very high; velocities of the order of 5 – 8 m/s are common and speeds up to 20 m/s have even be observed<ref>Nanayama, F. and Shigeno, K. 2006. Inflow and outflow facies from the 1993 tsunami in southwest Hokkaido. Sed. Geol. 187: 139–158</ref>. The destructive power of tsunamis is largely due to the many debris that are dragged by the flow. Upon travelling inland the flow gradually slows down. The largest debris are deposited first whereas the finest sediments are transported further inland. Sedimentary records showing upward fining deposits over large distances are a distinctive mark of tsunami events. The return flow to the sea (backwash) can also be very strong and dangerous; it follows the strongest topographic slope and is often concentrated in channels, with velocities that are often higher than during the uprush <ref>Le Roux, J.P. and Vargas, G. 2005. Hydraulic behavior of tsunami backflows: insights from their modern and ancient deposits. Environ. Geol. 49: 65–75</ref>. <br />
<br />
{| border="0"<br />
|-<br />
| valign="top"|<br />
[[File:Tsunami Phuket 2004 S.Kennedy.jpg|thumb|left|300px|Fig. 4a. Impact of the Indian Ocean tsunami of December 26, 2004 at Phuket, Thailand. Image S. Kennedy, Flickr creative commons.]]<br />
| valign="top"|<br />
[[File:Tsunami Japan 2011 Flickr J.Teramoto.jpg|thumb|left|300px|Fig. 4b. Destruction at the Honshu coast, Japan, by the tsunami of March 11, 2011. Image J. Teramoto, Flickr creative commons.]]<br />
| valign="top"|<br />
[[File:Tsunami Japan 2011 S.Yoshida.jpg|thumb|left|300px|Fig. 4c. Destruction at the Honshu coast, Japan, by the tsunami of March 11, 2011. Image Y. Yoshida, Flickr creative commons.]]<br />
|}<br />
<br />
<br />
==Why are tsunamis so devastating==<br />
The period of tsunami waves is typically in the range 300 – 6000 s (angular frequency in the order of 0.001 – 0.02 <math>s^{-1}</math>). Therefore, these waves are rather insensitive to the effect of earth's rotation, which corresponds to a frequency smaller than 0.00015 <math>s^{-1}</math>. Tsunami waves in the ocean have wavelengths typically in the order of 100 to 500 km and on the continental shelf in the order of 1 – 10 km. This implies that they are refracted and diffracted by seabed structures with spatial scales of these orders of magnitude. More specifically, this means that tsunami waves refract to the continental shelf and approach the shore more or less perpendicularly. The energy flux of tsunami waves is thus directed toward the coast. This contrasts with tidal waves that are too long for being refracted to the coast. Due to their very low frequency, tidal waves are bent along the coast by the effect of earth's rotation (see [[Coriolis and tidal motion in shelf seas]]). The energy flux of tidal waves, which is comparable in strength to the energy flux of tsunami waves, is therefore not directed towards the coast, but along the coast. Hence, the impact of tidal waves on the coast is much less than the impact of tsunami waves. <br />
Just like tsunami waves, wind-generated waves are also refracted to the coast. Their energy density on the ocean is generally higher than the energy density of tsunami waves. However, the energy propagation speed of wind waves is much lower and so is the corresponding energy flux. Hence, wind waves are much less amplified when travelling into shallow water than tsunami waves. Moreover, wind waves lose a great deal of their energy due to breaking in the surf zone before they reach the shore. This explains why tsunamis have a far more devastating effect on the coast compared to tidal and wind waves.<br />
<br />
<br />
==Tsunami observation and warning==<br />
Experimental measurements of real-life tsunamis running up the coast do not exist. Installing observation equipment at specific locations in anticipation of a tsunami makes no sense. Tsunami's are very rare events for each specific coastal location, even in areas that are very sensitive to submarine earthquakes. Experimental information about tsunamis that actually occurred is based on the effects observed in the coastal area after being hit by a tsunami. In some cases, eyewitness reports or amateur films are available. Although very important, this is insufficient for gaining in-depth understanding of the hydrodynamic processes that occur when a tsunami hits the coast. For this reason, understanding tsunamis is primarily based on modelling, as described in the next section. <br />
<br />
Tectonic activity that generates tsunamis is recorded by many seismic stations around the world. However, submarine earthquakes do not necessarily cause a tsunami. Tsunamis traveling across the ocean are very long waves of small amplitude that cannot be easily detected visually or by ships. For tsunami warning, an extensive network of monitoring stations has been installed in ocean areas where tsunamis can occur. The largest network is the DART system <ref> Deep-ocean Assessment and Reporting of Tsunamis, https://www.ndbc.noaa.gov/dart/dart.shtml </ref> consisting of an array of stations in the Pacific Ocean, see fig. 5a. Each station consists of a seabed pressure recorder that detects the passage of a tsunami. The data is sent by sonar signal to a moored buoy. This buoy sends a radio signal via satellite to the Pacific Tsunami Warning Center, see Fig. 5b. In this way, a tsunami traveling across the ocean can be detected and an early warning can be issued to countries where the tsunami will land, allowing timely evacuation of risk populations. The information collected by the monitoring network also enables to estimate the nature and intensity of the tsunami and the possible impact on the coast.<br />
<br />
{| border="0"<br />
|-<br />
| valign="top"|<br />
[[File:TsunamiMonitoringNetwork.jpg|thumb|left|400px|Fig. 5a. The global tsunami monitoring network.]]<br />
| valign="top"|<br />
[[File:TsunamiWarningDARTsystem.png|thumb|left|400px|Fig. 5b. The DART monitoring system. Image NOAA.]]<br />
|}<br />
<br />
<br />
==Tsunami models==<br />
Due to the lack of field observations, one has to rely on models for gaining insight into the hydrodynamic processes involved in tsunami events. The propagation of tsunami waves over the continental shelf and the shoreface can be simulated in hydraulic scale models based on Froude scaling, as long as boundary-layer processes are of minor importance. Scale effects occur when energy dissipation (wave breaking, bed friction) comes into play. This imposes a limitation on the simulation of the inland runup process in the laboratory. The same limitation applies to simple mathematical models that do not include wave breaking and friction. Detailed process-based numerical models are required for simulating these effects. A thorough model study of this type has been carried out by Larsen and Furman (2019)<ref name=LF></ref>.<br />
<br />
A major problem for predicting the impact of tsunamis lies in the fact that the initial tsunami-generating disturbance cannot be predicted and is generally not well known. When a tsunami wave is detected on the ocean, the time is too short for an accurate calculation of the impact before the tsunami lands on the coast. Only theoretical or semi-empirical relationships can be used. <br />
<br />
[[Image:TsunamiScheme.jpg|thumb|400px|left|Figure 6: Schematization of the shoreface and beach used in the tsunami runup model of Madsen and Schäfer (2010)<ref name=MS></ref>.]]<br />
<br />
Relationships for the tsunami runup height and runup velocity, validated with laboratory experiments and advanced numerical models, are based on the theoretical work of Madsen and Schäfer (2010)<ref name=MS></ref>. They solved analytically the non-linear shallow-water equations (mass and momentum balance without friction) over a sloping bed, <br />
<br />
<math>\Large\frac{\partial \zeta}{\partial t}\normalsize + \Large\frac{\partial}{\partial x}\normalsize [(D+\zeta -Sx)u] = 0 , \quad \Large\frac{\partial u}{\partial t}\normalsize + u \Large\frac{\partial u}{\partial x}\normalsize + g \Large\frac{\partial \zeta}{\partial x}\normalsize =0 , </math><br />
<br />
where <math>t</math> is time, <math>x</math> is the spatial coordinate in the propagation direction, <math>D</math> is the average shelf depth, <math>S</math> is the average shoreface and beach slope, <math>\zeta</math> is the surface elevation and <math>u</math> is the depth-averaged current velocity. The corresponding schematization is shown in Fig. 6. Madsen and Schäfer considered an incident tsunami wave of the form<br />
<br />
<math>\zeta(0,t) = A_0 \cos(\omega t) .</math> <br />
<br />
For a non-breaking tsunami wave they arrived at the following expressions for the maximum runup height <math>R</math> and the maximum runup velocity <math>V</math>:<br />
<br />
<math>R = 2 \pi^{3/4} A_0 \, (D / A_0)^{1/4} \, \xi^{-1/2} , \quad V = 2 \pi^{5/4} (A_0 / D) \sqrt{g A_0} \, \xi^{-3/2} . </math><br />
<br />
These simple expressions represent fairly well detailed numerical model results that include wave breaking, bed friction and turbulent energy dissipation<ref name=LF></ref>. The numerical model gives somewhat higher values of <math>R</math> and <math>V</math> for a sandy shore, but in practice the values will be lower due to energy dissipation on obstacles that are generally present the runup area. <br />
<br />
The numerical model <ref name=LF></ref> also provides results for <math>R</math> and <math>V</math> in the case of a breaking tsunami. These results are best approximated by<br />
<br />
<math>R = A_0 \xi , \quad V = 2 \sqrt{g A_0} .</math><br />
<br />
The first expression corresponds to the formula established by Hunt (1959) <ref>Hunt, I.A. 1959. Design of seawalls and breakwaters. J. Waterw. Harbors Division ASCE 85: 123–152</ref> for swash uprush (see the article [[Swash zone dynamics]]) and the second expression corresponds to the initial flow velocity after dam break (see the article [[Dam break flow]]). <br />
<br />
Non-breaking tsunamis occur for large <math>\xi</math>-values <math>\xi > \xi_b</math>, corresponding to a steep shoreface/beach slope and long-period tsunamis. Breaking tsunamis occur for small <math>\xi</math>-values <math>\xi < \xi_b</math>, corresponding to gentle shoreface/beach slope and short-period tsunamis. According to the numerical model <ref name=LF></ref>, <math>\xi_b \approx 3 (D / A_0)^{1/6}</math>.<br />
<br />
The above relationships are the result of recent studies (up to 2019) of tsunami irruption on a coast. However, further underpinning of the above results is needed, given that previous investigations produce results that differ in some respects <ref name=MG></ref>. Synolakis <ref> Synolakis, C. E. 1987. The runup of solitary waves. J. Fluid Mech. 185: 523–545 </ref> modeled the tsunami as a solitary wave of height <math>H</math> at the toe of the shoreface. This model, which was validated with laboratory measurements on steep slopes, yields for the runup height of a tsunami the relationship<br />
<br />
<math>R \approx 2.8 \, H \, S^{-1/2} \, (H/D)^{1/4} .</math><br />
<br />
A purely empirical rule for the maximum runup of a tsunami was proposed by Plafker (1964, unpublised). This rule states that the maximum runup will not exceed twice the height of the seafloor deformation resulting from a submarine earthquake <ref name=SB></ref>. <br />
<br />
<br />
==Related articles==<br />
: [[Swash zone dynamics]]<br />
: [[Dam break flow]]<br />
: [[Tidal bore dynamics]]<br />
<br />
<br />
==References==<br />
<references/></div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Testpage2&diff=76329Testpage22020-01-13T22:09:30Z<p>Dronkers J: </p>
<hr />
<div>Tsunami<br />
<br />
<br />
{{Definition|title=Tsunami <br />
|definition= Series of long waves caused by a strong local disturbance of the water mass. The wavelength is typically much larger than the wavelength of wind-generated waves and much smaller than the wavelength of tidal waves. }}<br />
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==Tsunami causes and occurrence==<br />
<br />
[[Image:RingofFireUSGS.jpg|thumb|300px|left|Figure 1: Ring of fire around the Pacific. Image USGS.]]<br />
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The occurrence of a tsunami can have several causes<ref name=RV>Röbke, R.B. and Vött, A. 2017. The tsunami phenomenon. Progress in Oceanography 159: 296–322</ref>. The main cause, responsible for the strongest tsunamis, are seaquakes (submarine earthquakes): the sudden uplift of the seabed due to shifting earth plates. This mainly occurs in subduction zones, where an earth plate slides under an adjacent earth plate causing vertical motion of the submarine crust along the subduction line. The most important subduction zones lie along the edges of the Pacific Ocean, the so-called ring of fire (see Fig. 1). The strength of the tsunami depends not only on the vertical and horizontal size of the seafloor uplift, but also on the speed at which the seafloor rises. The strongest response occurs when this speed is comparable to the local wave propagation speed. The tsunami wave radiates in both directions perpendicular to the subduction line. <br />
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A second important cause is submarine gravity mass wasting. Such slides can be triggered by seismic activity at a sloping seabed (e.g., the shelf break) that is covered with a thick layer of unconsolidated material. The tsunami wave propagates in the direction of the slide and is strongest if the speed of the debris flow is comparable to local wave propagation speed. Gas formation (methane) due to the anaerobic degradation of organic material can contribute to the loss of stability of the sediment layer on the sloping seabed <ref>Tinivella, U., Accaino, F. and della Vedova, B. 2008. Gas hydrates and active mud volcanism on the south Shetland continental margin, Antarctic Peninsula. Geo-Mar. Lett. 28: 97–106</ref>.<br />
Volcanic activity and subaerial landslides can also cause tsunamis, but these are usually not as strong. A tsunami can in rare cases result from the impact of a large meteorite.<br />
<br />
Another type of tsunamis, so-called meteotsunamis, can arise from atmospheric disturbances. Sudden local pressure fluctuations can generate a small setup or set-down of the water level that is amplified if the atmospheric front propagates at a speed comparable to the wave propagation speed or if the spatial/temporal scales coincide <ref>Monserrat, S., Vilibić, I. and Rabinovich, A.B. 2006. Meteotsunamis: atmospherically induced destructive ocean waves in the tsunami frequency band. Nat. Hazards Earth Syst. Sci. 6: 1035–1051</ref>. The amplitude of meteotsunamis is usually small, but it can increase strongly due to resonance effects in semi-closed basins (e.g., harbor seiches, which are damaging for moored ships).<br />
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==Tsunami characteristics==<br />
A tsunami usually consists of a number of waves (up to about ten) of different amplitude <ref>Grilli, S.T., Harris, J.C., Tajalli Bakhsh, T.S., Masterlark, T.L., Kyriakopoulos, C., Kirby, J.T. and Shi, F. 2013. Numerical simulation of the 2011 Tohoku tsunami based on a new transient FEM Co-seismic source: comparison to far- and near-field observations. Pure Appl. Geophys. 170: 1333–1359</ref>. The third, fourth or fifth wave are often the highest <ref> Murty, T.S. 1977. Seismic sea waves. Tsunamis. In: Stevenson, J.C. (Ed.), Bulletin of the Fisheries Research Board of Canada, vol. 198</ref>. The characteristic wave period is different for each tsunami, but usually much greater than the period of wind-driven waves (i.e., more than a few minutes) and much smaller than the tidal period (i.e., less than two hours). The wave height can be a few meters at the place of origin, but when the tsunami starts propagating over the ocean the wave height quickly becomes smaller and is then usually less than one meter<ref> Bolt, B.A., Horn, W.L., Macdonald, G.A. and Scott, R.F. 1975. Geological hazards. Earthquakes—Tsunamis—Volcanoes—Avalanches—Landslides—Floods. Springer, New York</ref>. The wavelength is much greater than the water depth and the energy loss during ocean propagation is small (approximately inversely proportional to the wavelength). The propagation speed <math>c</math> can therefore be approximated with the formula <math>c = \sqrt {gD}</math>, where <math>D</math> is the average depth and <math> g </math> the gravitational acceleration. Tsunamis travel at great speed across the ocean (<math>c</math> in the order of a few hundred m/s) covering distances of many thousands of kilometers without great energy loss.<br />
The energy flux <math> F </math> can be estimated with the formula <math>F = cE \approx (1/8) \rho g H ^ 2 \sqrt {gD}</math>, where <math>E</math> is the tsunami wave energy, <math> H </math> the tsunami wave height and <math>\rho</math> the water density. When the tsunami reaches the coastal zone, the water depth decreases sharply as does the propagation speed <math> c </math>. However, frictional energy dissipation being relatively modest, the energy flux <math>F</math> remains almost the same. This implies <math>H_{shore}/H_{ocean} \approx (D_{ocean}/D_{shore})^{1/4}</math>: the wave height <math>H</math> of the tsunami is strongly increased, up to about 5 times the wave height on the ocean. The wave height can be amplified even more in marine inlets, such as bays, fjords or harbours, where the tsunami energy flux is concentrated and accelerated due to strong funnel effects <ref name=RV></ref>. The tsunami waves are also distorted when entering shallow water; when the rear of the wave train is still traveling in deeper water it gets closer to the front of the wave train which is already travelling in shallow water. Differences in propagation speed of wave crest and wave trough contribute to steepening of the wave front on wide continental shelfs - wide compared to the tsunami wavelength.<br />
<br />
When the tsunami wave arrives at the coast it runs up the shoreface (schematically depicted in Fig. 6). If the slope is steep (the width of the shoreface being much smaller than the wavelength of the tsunami, i.e. less than 10 km), the tsunami 'feels' the shoreface as a straight wall. The tsunami is then almost completely reflected and the wave height is doubled. The tsunami floods the coast as a surging wave with a relatively low speed that can be outrun. The wave run-up is not much higher than the wave height on the foreshore.<br />
<br />
[[Image:Tsunami Phuket 2004.png|thumb|400px|left|Figure 2: The Indian Ocean tsunami of December 26, 2004, invading the coast at Phuket Thailand as a breaking bore. Picture from a camera lost on the beach. Image Flickr creative commons.]]<br />
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If the shoreface slope is gentle (the length of the foreshore being of the same order or greater than the wavelength), the tsunami transforms into an undular bore, with short waves riding on the main tsunami wave. When reaching the shore, the tsunami transforms further into a breaking bore (a wall of water, see Fig. 2) that propagates at great speed with a very fast rising water level. The wave run-up is much higher than the wave height at the toe of the shoreface (a factor of 2 and possibly more).<br />
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<br />
The above qualitative description suggests that the character of a tsunami is related to the surf similarity parameter <math>\xi</math> <ref name=MG> McGovern, D.J., Robinson, T., Chandler, I.D., Allsop, W. and Rossetto, T. 2018. Pneumatic long-wave generation of tsunami-length waveforms and their runup Coastal Engineering 138: 80–97</ref><ref name=LF>Larsen, B.E. and Fuhrman, D.R. 2019. Full-scale CFD simulation of tsunamis. Part 1: Model validation and run-up Coastal Engineering 151: 22–41</ref><ref name=MS>Madsen, P.A. and Schäffer, H.A. 2010. Analytical solutions for tsunami runup on a plane beach. J. Fluid Mech. 645: 27–57</ref>,<br />
<br />
<math>\xi = \Large\frac{S}{\sqrt{2 A_0/L_{\infty}}}\normalsize = \Large\frac{S}{\omega} \sqrt{\frac{\pi g}{A_0}}\normalsize , </math><br />
<br />
where <math>A_0</math> is the tsunami wave height above mean sea level at the toe of the shoreface slope, <math>L_{\infty} = g T^2/(2 \pi)</math> is the tsunami wave length at infinite depth, <math>S</math> is the shoreface slope and <math>\omega</math> is the tsunami wave period. Surging waves correspond to high values of <math>\xi</math> and breaking waves to low values. <br />
<br />
[[Image:BandAcehTsunamiLeadingDepression.jpg|thumb|300px|left|Figure 3: Retreating shoreline before arrival of the major wave of the Indian Ocean tsunami at Banda Aceh on December 26, 2004. Image C.E. Synolakis <ref name=SB>Synolakis, C.E. and Bernard, E.N. 2006. Tsunami science before and beyond Boxing Day 2004. Phil. Trans. R. Soc. A. 364: 2231–2265</ref>.]]<br />
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<br />
A distinction is often made between two types of tsunamis: tsunamis where the largest wave crest precedes the largest wave trough (sometimes called leading-elevation N-wave or LEN-wave) and tsunamis where the largest wave crest is preceded by the largest wave trough (sometimes called leading-depression N-wave or LDN-wave). Both types of tsunami occur in practice. In case of a LDN-wave, the sea retreats over a large distance and part of the shoreface falls dry before arrival of the wave crest, see Fig. 3. This is an important signal for bathers that a high tsunami wave is approaching. A LDN-wave approaches the shore at a lower speed than a similar LEN-wave, but the runup speed on land is in both cases of the same order. <br />
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<br />
==Tsunami impact==<br />
Tsunamis can cause enormous damage to coastal infrastructure, crushing houses, deracinating trees and making many casualties, see Fig. 4. From historical records it has been estimated that more than a million people have been killed worldwide by tsunamis <ref>National Geophysical Data Center/World Data Service, 2015. Global historical tsunami database. Tsunami event data. <http://www.ngdc.noaa.gov/hazard/tsu_db.shtml></ref>. In low-lying coastal areas (less than 10 m elevation above mean sea level) tsunamis can penetrate several kilometers inland. There are even records of tsunamis that have penetrated several tens of kilometers inland and have reached levels of several tens of meters. The flood water volume is approximately equal to the water volume above beach level of the incident tsunami wave <ref>Bryant, E.A., 2008. Tsunami: The Underrated Hazard, second ed. Springer, Berlin</ref>. Runup velocities of strong tsunamis are very high; velocities of the order of 5 – 8 m/s are common and speeds up to 20 m/s have even be observed<ref>Nanayama, F. and Shigeno, K. 2006. Inflow and outflow facies from the 1993 tsunami in southwest Hokkaido. Sed. Geol. 187: 139–158</ref>. The destructive power of tsunamis is largely due to the many debris that are dragged by the flow. Upon travelling inland the flow gradually slows down. The largest debris are deposited first whereas the finest sediments are transported further inland. Sedimentary records showing upward fining deposits over large distances are a distinctive mark of tsunami events. The return flow to the sea (backwash) can also be very strong and dangerous; it follows the strongest topographic slope and is often concentrated in channels, with velocities that are often higher than during the uprush <ref>Le Roux, J.P. and Vargas, G. 2005. Hydraulic behavior of tsunami backflows: insights from their modern and ancient deposits. Environ. Geol. 49: 65–75</ref>. <br />
<br />
{| border="0"<br />
|-<br />
| valign="top"|<br />
[[File:Tsunami Phuket 2004 S.Kennedy.jpg|thumb|left|300px|Fig. 4a. Impact of the Indian Ocean tsunami of December 26, 2004 at Phuket, Thailand. Image S. Kennedy, Flickr creative commons.]]<br />
| valign="top"|<br />
[[File:Tsunami Japan 2011 Flickr J.Teramoto.jpg|thumb|left|300px|Fig. 4b. Destruction at the Honshu coast, Japan, by the tsunami of March 11, 2011. Image J. Teramoto, Flickr creative commons.]]<br />
| valign="top"|<br />
[[File:Tsunami Japan 2011 S.Yoshida.jpg|thumb|left|300px|Fig. 4c. Destruction at the Honshu coast, Japan, by the tsunami of March 11, 2011. Image Y. Yoshida, Flickr creative commons.]]<br />
|}<br />
<br />
<br />
==Why are tsunamis so devastating==<br />
The period of tsunami waves is typically in the range 300 – 6000 s (angular frequency in the order of 0.001 – 0.02 <math>s^{-1}</math>). Therefore, these waves are rather insensitive to the effect of earth's rotation, which corresponds to a frequency smaller than 0.00015 <math>s^{-1}</math>. Tsunami waves in the ocean have wavelengths typically in the order of 100 to 500 km and on the continental shelf in the order of 1 – 10 km. This implies that they are refracted and diffracted by seabed structures with spatial scales of these orders of magnitude. More specifically, this means that tsunami waves refract to the continental shelf and approach the shore more or less perpendicularly. The energy flux of tsunami waves is thus directed toward the coast. This contrasts with tidal waves that are too long for being refracted to the coast. Due to their very low frequency, tidal waves are bent along the coast by the effect of earth's rotation (see [[Coriolis and tidal motion in shelf seas]]). The energy flux of tidal waves, which is comparable in strength to the energy flux of tsunami waves, is therefore not directed towards the coast, but along the coast. Hence, the impact of tidal waves on the coast is much less than the impact of tsunami waves. <br />
Just like tsunami waves, wind-generated waves are also refracted to the coast. Their energy density on the ocean is generally higher than the energy density of tsunami waves. However, the energy propagation speed of wind waves is much lower and so is the corresponding energy flux. Hence, wind waves are much less amplified when travelling into shallow water than tsunami waves. Moreover, wind waves lose a great deal of their energy due to breaking in the surf zone before they reach the shore. This explains why tsunamis have a far more devastating effect on the coast compared to tidal and wind waves.<br />
<br />
<br />
==Tsunami observation and warning==<br />
Experimental measurements of real-life tsunamis running up the coast do not exist. Installing observation equipment at specific locations in anticipation of a tsunami makes no sense. Tsunami's are very rare events for each specific coastal location, even in areas that are very sensitive to submarine earthquakes. Experimental information about tsunamis that actually occurred is based on the effects observed in the coastal area after being hit by a tsunami. In some cases, eyewitness reports or amateur films are available. Although very important, this is insufficient for gaining in-depth understanding of the hydrodynamic processes that occur when a tsunami hits the coast. For this reason, understanding tsunamis is primarily based on modelling, as described in the next section. <br />
<br />
Tectonic activity that generates tsunamis is recorded by many seismic stations around the world. However, submarine earthquakes do not necessarily cause a tsunami. Tsunamis traveling across the ocean are very long waves of small amplitude that cannot be easily detected visually or by ships. For tsunami warning, an extensive network of monitoring stations has been installed in ocean areas where tsunamis can occur. The largest network is the DART system <ref> Deep-ocean Assessment and Reporting of Tsunamis, https://www.ndbc.noaa.gov/dart/dart.shtml </ref> consisting of an array of stations in the Pacific Ocean, see fig. 5a. Each station consists of a seabed pressure recorder that detects the passage of a tsunami. The data is sent by sonar signal to a moored buoy. This buoy sends a radio signal via satellite to the Pacific Tsunami Warning Center, see Fig. 5b. In this way, a tsunami traveling across the ocean can be detected and an early warning can be issued to countries where the tsunami will land, allowing timely evacuation of risk populations. The information collected by the monitoring network also enables to estimate the nature and intensity of the tsunami and the possible impact on the coast.<br />
<br />
{| border="0"<br />
|-<br />
| valign="top"|<br />
[[File:TsunamiMonitoringNetwork.jpg|thumb|left|400px|Fig. 5a. The global tsunami monitoring network.]]<br />
| valign="top"|<br />
[[File:TsunamiWarningDARTsystem.png|thumb|left|400px|Fig. 5b. The DART monitoring system. Image NOAA.]]<br />
|}<br />
<br />
<br />
==Tsunami models==<br />
Due to the lack of field observations, one has to rely on models for gaining insight into the hydrodynamic processes involved in tsunami events. The propagation of tsunami waves over the continental shelf and the shoreface can be simulated in hydraulic scale models based on Froude scaling, as long as boundary-layer processes are of minor importance. Scale effects occur when energy dissipation (wave breaking, bed friction) comes into play. This imposes a limitation on the simulation of the inland runup process in the laboratory. The same limitation applies to simple mathematical models that do not include wave breaking and friction. Detailed process-based numerical models are required for simulating these effects. A thorough model study of this type has been carried out by Larsen and Furman (2019)<ref name=LF></ref>.<br />
<br />
A major problem for predicting the impact of tsunamis lies in the fact that the initial tsunami-generating disturbance cannot be predicted and is generally not well known. When a tsunami wave is detected on the ocean, the time is too short for an accurate calculation of the impact before the tsunami lands on the coast. Only theoretical or semi-empirical relationships can be used. <br />
<br />
[[Image:TsunamiScheme.jpg|thumb|400px|left|Figure 6: Schematization of the shoreface and beach used in the tsunami runup model of Madsen and Schäfer (2010)<ref name=MS></ref>.]]<br />
<br />
Relationships for the tsunami runup height and runup velocity, validated with laboratory experiments and advanced numerical models, are based on the theoretical work of Madsen and Schäfer (2010)<ref name=MS></ref>. They solved analytically the non-linear shallow-water equations (mass and momentum balance) over a sloping bed, <br />
<br />
<math>\Large\frac{\partial \zeta}{\partial t}\normalsize + \Large\frac{\partial}{\partial x}\normalsize [(D+\zeta -Sx)u] = 0 , \quad \Large\frac{\partial u}{\partial t}\normalsize + u \Large\frac{\partial u}{\partial x}\normalsize + g \Large\frac{\partial \zeta}{\partial x}\normalsize =0 , </math><br />
<br />
where <math>t</math> is time, <math>x</math> is the spatial coordinate in the propagation direction, <math>D</math> is the average shelf depth, <math>S</math> is the average shoreface and beach slope, <math>\zeta</math> is the surface elevation and <math>u</math> is the depth-averaged current velocity. The corresponding schematization is shown in Fig. 6. Madsen and Schäfer considered an incident tsunami wave of the form<br />
<br />
<math>\zeta(0,t) = A_0 \cos(\omega t) .</math> <br />
<br />
For a non-breaking tsunami wave they arrived at the following expressions for the maximum runup height <math>R</math> and the maximum runup velocity <math>V</math>:<br />
<br />
<math>R = 2 \pi^{3/4} A_0 (D / A_0)^{1/4} \xi^{-1/2} , \quad V = 2 \pi^{5/4} (A_0 / D) \sqrt{g A_0} \xi^{-3/2} . </math><br />
<br />
These simple expressions represent fairly well detailed numerical model results that include wave breaking, bed friction and turbulent energy dissipation<ref name=LF></ref>. The numerical model gives somewhat higher values of <math>R</math> and <math>V</math>, but in practice the values might be lower due to energy dissipation on obstacles that are generally present the runup area. <br />
<br />
The numerical model <ref name=LF></ref> also provides results for <math>R</math> and <math>V</math> in the case of a breaking tsunami. These results are best approximated by<br />
<br />
<math>R = A_0 \xi , \quad V = 2 \sqrt{g A_0} .</math><br />
<br />
The first expression corresponds to the formula established by Hunt (1959) <ref>Hunt, I.A. 1959. Design of seawalls and breakwaters. J. Waterw. Harbors Division ASCE 85: 123–152</ref> for swash uprush (see the article [[Swash zone dynamics]]) and the second expression corresponds to the initial flow velocity after dam break (see the article [[Dam break flow]]). <br />
<br />
Non-breaking tsunamis occur for large <math>\xi</math>-values <math>\xi > \xi_b</math>, corresponding to a steep shoreface/beach slope and long-period tsunamis. Breaking tsunamis occur for small <math>\xi</math>-values <math>\xi < \xi_b</math>, corresponding to gentle shoreface/beach slope and short-period tsunamis. According to the numerical model <ref name=LF></ref>, <math>\xi_b \approx 3 (D / A_0)^{1/6}</math>.<br />
<br />
The above relationships are the result of recent studies (up to 2019) of tsunami irruption on a coast. However, further underpinning of the above results is needed, given that previous investigations produce results that differ in some respects <ref name=MG></ref>. Synolakis <ref> Synolakis, C. E. 1987. The runup of solitary waves. J. Fluid Mech. 185: 523–545 </ref> modeled the tsunami as a solitary wave of height <math>H</math>. This model, which was validated with other laboratory measurements, yields for the runup height of a tsunami the relationship<br />
<br />
<math>R = 2.8 H S (H/D)^{5/4} .</math><br />
<br />
A purely empirical rule for the maximum runup of a tsunami was proposed by Plafker (1964, unpublised). This rule states that the maximum runup will not exceed twice the height of the seafloor deformation resulting from a submarine earthquake <ref name=SB></ref>. <br />
<br />
<br />
==Related articles==<br />
: [[Swash zone dynamics]]<br />
: [[Dam break flow]]<br />
: [[Tidal bore dynamics]]<br />
<br />
<br />
==References==<br />
<references/></div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=File:TsunamiScheme.jpg&diff=76328File:TsunamiScheme.jpg2020-01-13T18:27:13Z<p>Dronkers J: Schematization of the shoreface and beach used in the tsunami runup model of Madsen and Schäfer (2010).</p>
<hr />
<div>== Summary ==<br />
Schematization of the shoreface and beach used in the tsunami runup model of Madsen and Schäfer (2010).</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=File:TsunamiMonitoringNetwork.jpg&diff=76327File:TsunamiMonitoringNetwork.jpg2020-01-13T18:25:30Z<p>Dronkers J: The global tsunami monitoring network.</p>
<hr />
<div>== Summary ==<br />
The global tsunami monitoring network.</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=File:TsunamiWarningDARTsystem.png&diff=76326File:TsunamiWarningDARTsystem.png2020-01-13T18:24:46Z<p>Dronkers J: The DART monitoring system. Image NOAA.</p>
<hr />
<div>== Summary ==<br />
The DART monitoring system. Image NOAA.</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=File:Tsunami_Japan_2011_S.Yoshida.jpg&diff=76325File:Tsunami Japan 2011 S.Yoshida.jpg2020-01-13T18:23:48Z<p>Dronkers J: Destruction at the Honshu coast, Japan, by the tsunami of March 11, 2011. Image Y. Yoshida, Flickr creative commons.</p>
<hr />
<div>== Summary ==<br />
Destruction at the Honshu coast, Japan, by the tsunami of March 11, 2011. Image Y. Yoshida, Flickr creative commons.</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=File:Tsunami_Japan_2011_Flickr_J.Teramoto.jpg&diff=76324File:Tsunami Japan 2011 Flickr J.Teramoto.jpg2020-01-13T18:23:13Z<p>Dronkers J: Destruction at the Honshu coast, Japan, by the tsunami of March 11, 2011. Image J. Teramoto, Flickr creative commons.</p>
<hr />
<div>== Summary ==<br />
Destruction at the Honshu coast, Japan, by the tsunami of March 11, 2011. Image J. Teramoto, Flickr creative commons.</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=File:Tsunami_Phuket_2004_S.Kennedy.jpg&diff=76323File:Tsunami Phuket 2004 S.Kennedy.jpg2020-01-13T18:22:28Z<p>Dronkers J: Impact of the Indian Ocean tsunami of December 26, 2004 at Phuket, Thailand. Image S. Kennedy, Flickr creative commons.</p>
<hr />
<div>== Summary ==<br />
Impact of the Indian Ocean tsunami of December 26, 2004 at Phuket, Thailand. Image S. Kennedy, Flickr creative commons.</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=File:BandAcehTsunamiLeadingDepression.jpg&diff=76322File:BandAcehTsunamiLeadingDepression.jpg2020-01-13T18:21:29Z<p>Dronkers J: Retreating shoreline before arrival of the major wave of the Indian Ocean tsunami at Banda Aceh on December 26, 2004.</p>
<hr />
<div>== Summary ==<br />
Retreating shoreline before arrival of the major wave of the Indian Ocean tsunami at Banda Aceh on December 26, 2004.</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=File:Tsunami_Phuket_2004.png&diff=76321File:Tsunami Phuket 2004.png2020-01-13T18:20:10Z<p>Dronkers J: The Indian Ocean tsunami of December 26, 2004, invading the coast at Phuket Thailand as a breaking bore.</p>
<hr />
<div>== Summary ==<br />
The Indian Ocean tsunami of December 26, 2004, invading the coast at Phuket Thailand as a breaking bore.</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=File:RingofFireUSGS.jpg&diff=76320File:RingofFireUSGS.jpg2020-01-13T18:18:47Z<p>Dronkers J: Ring of fire around the Pacific.</p>
<hr />
<div>== Summary ==<br />
Ring of fire around the Pacific.</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Talk:Dune_stabilisation&diff=76319Talk:Dune stabilisation2020-01-12T11:39:01Z<p>Dronkers J: Created page with "An amendment by Gwen Potter has been inserted in the second allinea of the section "Background"."</p>
<hr />
<div>An amendment by Gwen Potter has been inserted in the second allinea of the section "Background".</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Dune_stabilisation&diff=76318Dune stabilisation2020-01-12T11:33:29Z<p>Dronkers J: </p>
<hr />
<div>[[Dune]]s are a natural coastal feature on moderately exposed and exposed coasts. [[Dune]]s are formed by the sand, which blows inland from the beach and is deposited in the area behind the coastline. <br />
<br />
==Background==<br />
During [[Extreme storms|storm surge events]], the foot of the [[dune]]s can be eroded but the [[dune]]s act as a very flexible buffer zone, which protects the hinterland from [[erosion]] and flooding. The eroded material supplies material to the littoral budget minimising the general erosion along the entire section of shoreline. During the storm and also during more normal events, sand will be transported inland, sometimes in connection with the formation of wind alleys in the dune row. After the storm, the damaged [[dune]] will gradually be built up again, maybe slightly more inland. This means that a dune acts as a natural flexible coast protection and sea defence measures. It moves backwards parallel with the eroding coastline and at the same time it maintains its form and volume as well as a wide beach. This is a natural quasi-equilibrium situation. The [[erosion]] of [[dune]]s as a result of a severe storm surge is also referred to as [[dune erosion]]. <br />
<br />
However, the natural balance will shift if the dune vegetation is damaged by undergrazing, overgrazing or if beach-users, etc. generate too much traffic. Some management such as golf course management typically fails to allow a sand dune system to move naturally. Damaging activity may cause the dunes to degrade, resulting in loss of the protection provided by the natural dunes. At the same time, sand blowing inland can cause various kinds of damage to agriculture where adaptation to this natural movement of the dune does not occur. Consequently, authorities normally tend to protect dunes by regulating their use.<br />
<br />
In some cases authorities have been very eager to protect the [[dune]]s by planting [[marram grass]] and placing fences or fascines (placing of pine or spruce branches) in the wind alleys to trap the sand <ref>NSW 2001. Coastal Dune Management: A Manual of Coastal Dune Management and Rehabilitation Techniques. New South Wales, Department of Land and Water Conservation, Australia, http://www.environment.nsw.gov.au/resources/coasts/coastal-dune-mngt-manual.pdf </ref><ref>USACE 2008. Coastal Engineering Manual. Part V, Ch. 7. Coastal Engineering for Environmental Enhancement pp. V.7.17-V.7.21. https://www.publications.usace.army.mil/USACE-Publications/Engineer-Manuals/u43544q/636F617374616C20656E67696E656572696E67206D616E75616C/</ref>. However, in some cases, this has resulted in complete fixing of the dune position and an unnatural growth in height. Consequently, the flexibility of the natural dune is lost resulting in a gradual disappearance of the [[dune]] due to erosion, whereby the protection, provided by the natural [[dune]] system, is lost.<br />
<br />
==Method==<br />
[[Image:Marram planting.jpg|thumb|Fig. 1. Marram planting and the placing of spruce fascines in wind alleys (Danish Coastal Authority<ref>Danish Coastal Authority, 1998. "Menneske, Hav, Kyst og Sand". (in Danish), (Man, Sea Coast and Sand in English). Kystinspektoratet 1973-1998.</ref>).]]<br />
Planting marram grass and setting up spruce fascines for trapping of sand and enhancement of [[dune]] build up. Larger wind alleys can also be filled artificially prior to planting. However, as mentioned above, the protection should not be so comprehensive that it completely fixes the dunes.<br />
<br />
Newly planted vegetation in particular can be strengthened by using fertiliser.<br />
<br />
Restrictions for their use can also protect the [[dune]]s. Grazing in dune areas is prohibited in most countries, and authorities often limit public access. Such restrictions may regulate the traffic in the dunes, e.g. by prohibiting motor traffic. Different options are paved walking passages in areas near parking lots and fencing fragile newly planted areas.<br />
<br />
==Functional characteristic==<br />
[[Dune]] stabilisation is a sustainable protection measure, enhancing the natural protection ability of dune areas. It protects against wave and storm surge attack and at the same time it preserves the natural coastal landscape, if performed moderately. Dune stabilisation requires a planned and co-ordinated effort. <br />
<br />
==Applicability==<br />
[[Dune]] stabilisation is applicable on all coastal types where natural dunes occur. This is especially the case on moderately exposed to exposed coasts with perpendicular to very oblique wave (wind) attacks. <br />
<br />
Artificial [[dune]]s are also used as a sea defence structure.<br />
<br />
<br />
==Related articles==<br />
:[[Deflation]]<br />
:[[Dune erosion]]<br />
:[[Hard coastal protection structures]]<br />
<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
==Further reading==<br />
:Mangor, Karsten. 2004. “Shoreline Management Guidelines”. DHI Water and Environment, 294pg.<br />
<br />
<br />
<br />
{{author<br />
|AuthorID=13331<br />
|AuthorFullName=Mangor, Karsten<br />
|AuthorName=Karsten}}<br />
<br />
[[Category:Coastal protection]]<br />
[[Category:Soft coastal interventions]]<br />
[[Category:Beaches]]</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=File:DamBreakFlowDerivation.png&diff=76317File:DamBreakFlowDerivation.png2020-01-02T20:27:11Z<p>Dronkers J: Derivation of the solution for frictionless dam break flow.</p>
<hr />
<div>== Summary ==<br />
Derivation of the solution for frictionless dam break flow.</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Testpage1&diff=76315Testpage12020-01-01T13:20:16Z<p>Dronkers J: </p>
<hr />
<div>=Dam break flow=<br />
<br />
<br />
==Introduction==<br />
<br />
[[image:Dijkdoorbraak1953.png|thumb|left|300px|Fig. 1. Sea dikes protecting low-lying polders in the Netherlands were breached during the extreme storm surge of 31 January 1953.]] <br />
<br />
<br />
<br />
<br />
<br />
Dam failure can lead to catastrophic situations. Most dam break tragedies are known for dam collapse in mountainous rivers. The failure of sea dikes can also cause major disasters, although the level difference is not that great. A dramatic example is the failure of more than fifty sea dikes in the Netherlands during the extreme storm surge of 1953, see figure 1. Many of these dikes protected land lying below the average sea level, while the storm surge level exceeded more than five meters. Rapid flooding killed many people who were unable to flee to safe places in time. This article does not discuss the causes of dam failure, but the resulting flood wave.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
[[image:DamBreakFlowPrinciple.jpg|thumb|center|600px|Fig. 2. Left panel: Schematic representation of water retention behind a dam. Right panel: Positive downstream and negative upstream surges following instantaneous dam removal.]]<br />
<br />
<br />
The consequences of dam failure have been studied for more than a century. It nevertheless remains a challenging topic due to the high non-linearity of the flood wave propagation. The problem can be tackled with numerical models, but rough estimates and insight into the tidal wave dynamics can be obtained with analytical solution methods.<br />
<br />
<br />
==Frictionless dam-break flow: analytical solution==<br />
<br />
Analytical solutions relate to idealized situations as depicted in Fig. 2. The initial situation consists of an infinite reservoir with a water level that is <math> h_0 </math> higher than the horizontal ground level downstream of the dam. Dam break is simulated by instantaneous removal of the dam. This causes a positive surge in the positive <math> x </math>-direction and a negative surge in the negative <math> x </math>-direction. The floor is dry in front of the positive surge and the body of water behind the negative surge is undisturbed: water level <math> h_0 </math> and current speed <math> u = 0 </math>.<br />
<br />
[[image:SouthForkDamFailure1889.jpg|thumb|left|300px|Fig. 3. The earth-filled South Fork Dam on Lake Conemaugh (Pennsylvania, US) collapsed in 1889, killing 2,209 people in downstream villages.]]<br />
<br />
<br />
<br />
<br />
<br />
<br />
The study of the dam break-flow was triggered by several dam failures in the 19th century, in particular the breach of the South Fork Dam in Pennsylvania (USA) in 1889, Fig. 3. Three years later Ritter <ref> Ritter, A. 1892. Die Fortpflanzung der Wasserwellen. Zeitschrift des Vereines Deutscher Ingenieure 36: 947-954 </ref> published an exact analytical solution for dam-break flow by assuming that frictional effects can be ignored. The derivation is given in box 1. According to this solution, the tip of the positive surge advances at high speed (supercritical flow) given by <math> u_f = 2 c_0</math>, where <math>c_0 = \sqrt {gh_0}</math> and <math> g </math> is the gravitational acceleration. The shape of the positive and negative wave is a concave-up parabola,<br />
<br />
<math>h(x,t)= h_0, \; x/t<-c_0; \quad h(x,t)= \Large\frac{h_0}{9}\normalsize \; (2 - \Large\frac{x}{c_0 t}\normalsize)^2 , \, -c_0<x/t<2c_0; \quad h(x,t)= 0, \, x/t>2c_0 , \qquad (1)</math><br />
<br />
see Fig. 4. The same figure also shows the shape of the dam break wave that was observed in laboratory experiments. For small values of <math> x / t </math>, the frictionless solution corresponds fairly well with the observations. However, the front zone is different: the shape is a bull nose, rather than a sharp edge. The front also advances more slowly; the speed of the front decreases with time and is closer to <math> u_f = c_0 </math> than to <math> u_f = 2 c_0 </math>. The reason for this difference is the neglect of frictional effects that are important in the thin fluid layer near the front.<br />
<br />
<br />
[[image:DamBreakFlowDerivation.png|thumb|center|900px|Box 1. Derivation of the solution for frictionless dam break flow.]]<br />
<br />
<br />
==Dam-break flow with friction==<br />
<br />
[[image:DamBreakWaveProfiles.jpg|thumb|left|400px|Fig. 4. Wave profile after dam break. The red curve corresponds to the frictionless solution Eq. 1. The blue band represents data from different laboratory experiments performed at times <math>\small t \sim (40-80) \, \sqrt {h_0 / g}\normalsize </math> after removal of the dam <ref>Dressler, R. 1954. Comparison of theories and experiments for the hydraulic dam-break wave. Proc. Int. Assoc. Scientific Hydrology Assemblée Générale, Rome, Italy 3 (38)M 319–328</ref> <ref>Schoklitsch, A. 1917. Über Dambruchwellen. Kaiserliche Akademie der Wissenschaften, Wien, Mathematisch-Naturwissenschaftliche Klasse, Sitzungberichte IIa, 126: 1489–1514</ref><ref>Cavaillé,Y. 1965. Contribution à l’étude de l’écoulement variable accompagnant la vidange brusque d’une retenue. Publ. Scient. et Techn. du Ministère de l’Air, 410, Paris, France, 165</ref>. The frictionless solution only depends on <math>x/t</math>. Observed wave profiles also depend on time <math>t</math> because of the decreasing wave tip speed.]]<br />
<br />
<br />
When friction terms are included in the flow equations, there is no exact analytical solution. It is generally assumed that the frictionless flow equations are approximately valid in a short period after dam break and for small values of <math>x / (c_0 t) </math>. In the front zone, where the water depth is small, the momentum balance is dominated by frictional momentum dissipation. If the inertia terms <math>\partial u / \partial t + u \partial u / \partial x </math> in the momentum equation are ignored, then the current in the front region is mainly determined by the balance of gravitational acceleration <math> g \partial h / \partial x </math> and shear stress <math>\tau</math>, the latter term being proportional to the square of the flow velocity<ref>Dressler, R.F. 1952. Hydraulic resistance effect upon the dambreak functions. J. Res. Natl. Bureau of Standards, 49(3): 217–225</ref><ref>Whitham, G.B. 1955. The effects of hydraulic resistance in the dam-break problem. Proc. Roy. Soc. of London, Serie A, 227: 399–407</ref><ref>Hogg, A.J. and Pritchard, D. 2004. The effects of hydraulic resistance on dam-break and other shallow inertial flows. J. Fluid Mech. 501: 179–212</ref><ref name=C09>Chanson, H. 2009. Application of the method of characteristics to the dam break wave problem. Journal of Hydraulic Research 47: 41–49</ref>. With such models the shape of the wave front is given by <math>h(s) \propto s^n, \; n=1/2</math>, where <math>s</math> is the distance measured from the wave front. The wave front speed <math>u_f</math> decreases with time. At large times <math>t>>t_{\infty}</math>, the wave front speed varies approximately as <math>u_f \approx c_0 \sqrt{t_{\infty}/t}</math> <ref name=C09></ref>. Here, <math>t_{\infty} = \sqrt{h_0/g}/(3 c_D)</math> and <math>c_D</math> is the friction coefficient (value in the range <math>\approx (1-5)\, 10^{-3}</math>). A more elaborate model of the frictional boundary layer near the wave front was studied by Nielsen (2018) <ref name=PN>Nielsen, P. 2018 Bed shear stress, surface shape and velocity field near the tips of dam-breaks, tsunami and wave runup velocity. Coastal Engineering 138: 126–131</ref>. According to this model, the wavefront is even more blunt, corresponding to <math> n = 1/4 </math>, which agrees well with laboratory experiments. This model also reveals a strong downward velocity component at the wavefront, which can contribute to the dislodging of particles from the sediment bed <ref name = PN> </ref>. This may explain the high near-bed of suspended concentrations associated with propagating surges observed in the field<ref>Khezri, N. and Chanson, H. 2012. Inception of bed load motion beneath a bore. Geomorphology 153: 39–47</ref>, see also the article [[Tidal bore dynamics]]. <br />
<br />
<br />
For situations that can be schematically represented by simple geometries, parametric models have been developed based on data for a large number of previous dam breaks<ref> Wang, B., Chen, Y., Wu, C., Peng, Y., Song, J., Liu, W. and Liu, X. 2018. Empirical and semi-analytical models for predicting peak outflows caused by embankment dam failures. Journal of Hydrology 562: 692–702</ref>. <br />
<br />
<br />
==Numerical models==<br />
<br />
The analytical methods for describing dam-break flow provide a qualitative picture and some first-order estimates for the wave profile and wave speed. They may only be used in situations that can be represented schematically by a simple prismatic channel. In most actual field situations, the dam-break flow must be modeled numerically. Detailed simulation of the forward and backward wave fronts requires 3D models of the Boussinesq type, taking into account vertical fluid accelerations<ref>Castro-Orgaz, O. and Chanson, H. 2017. Ritter’s dry-bed dam-break flows: positive and negative wave dynamics. Environ Fluid Mech (2017) 17:665–694</ref>. To correctly model the strong temporal and spatial gradients of the surging wave, a fine computational grid is required, with resulting long computer times. <br />
<br />
<br />
<br />
==References==<br />
<references/></div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Testpage1&diff=76313Testpage12019-12-31T16:25:28Z<p>Dronkers J: </p>
<hr />
<div>=Dam break flow=<br />
<br />
<br />
==Introduction==<br />
<br />
[[image:Dijkdoorbraak1953.png|thumb|left|300px|Fig. 1. Sea dikes protecting low-lying polders in the Netherlands were breached during the extreme storm surge of 31 January 1953.]] <br />
<br />
<br />
<br />
<br />
<br />
Dam failure can lead to catastrophic situations. Most dam break tragedies are known for dam collapse in mountainous rivers. The failure of sea dikes can also cause major disasters, although the level difference is not that great. A dramatic example is the failure of more than fifty sea dikes in the Netherlands during the extreme storm surge of 1953, see figure 1. Many of these dikes protected land lying below the average sea level, while the storm surge level exceeded more than five meters. Rapid flooding killed many people who were unable to flee to safe places in time. This article does not discuss the causes of dam failure, but the resulting tidal wave.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
[[image:DamBreakFlowPrinciple.jpg|thumb|center|600px|Fig. 2. Left panel: Schematic representation of water retention behind a dam. Right panel: Positive downstream and negative upstream surges following instantaneous dam removal.]]<br />
<br />
<br />
The consequences of dam failure have been studied for more than a century. It nevertheless remains a challenging topic due to the high non-linearity of the flood wave propagation. The problem can be tackled with numerical models, but rough estimates and insight into the tidal wave dynamics can be obtained with analytical solution methods.<br />
<br />
<br />
==Frictionless dam-break flow: analytical solution==<br />
<br />
Analytical solutions relate to idealized situations as depicted in Fig. 2. The initial situation consists of an infinite reservoir with a water level that is <math> h_0 </math> higher than the horizontal ground level downstream of the dam. Dam break is simulated by instantaneous removal of the dam. This causes a positive surge in the positive <math> x </math>-direction and a negative surge in the negative <math> x </math>-direction. The floor is dry in front of the positive surge and the body of water behind the negative surge is undisturbed: water level <math> h_0 </math> and current speed <math> u = 0 </math>.<br />
<br />
[[image:SouthForkDamFailure1889.jpg|thumb|left|300px|Fig. 3. The earth-filled South Fork Dam on Lake Conemaugh (Pennsylvania, US) collapsed in 1889, killing 2,209 people in downstream villages.]]<br />
<br />
<br />
<br />
<br />
<br />
<br />
The study of the dam break-flow was initiated by several dam failures in the 19th century, in particular the breach of the South Fork Dam in Pennsylvania (USA) in 1889, Fig. 3. Three years later Ritter <ref> Ritter, A. 1892. Die Fortpflanzung der Wasserwellen. Zeitschrift des Vereines Deutscher Ingenieure 36: 947-954 </ref> published an exact analytical solution for dam-break flow by assuming that frictional effects can be ignored. The derivation is given in box 1. According to this solution, the tip of the positive surge advances at high speed (supercritical flow) given by <math> u_f = 2 c_0</math>, where <math>c_0 = \sqrt {gh_0}</math> and <math> g </math> is the gravitational acceleration. The shape of the positive and negative wave is a concave-up parabola,<br />
<math>h(x,t)= h_0, \; x/t<-c_0; \quad h(x,t)= \Large\frac{h_0}{9}\normalsize \; (2 - \Large\frac{x}{c_0 t}\normalsize) , \, -c_0<x/t<2c_0; \quad h(x,t)= 0, \, x/t>2c_0 , \qquad (1)</math><br />
<br />
see Fig. 4. The same figure also shows the shape of the dam break wave that was observed in laboratory experiments. For small values of <math> x / t </math>, the frictionless solution corresponds fairly well with the observations. However, the front zone is different: the shape is a bull nose, rather than a sharp edge. The front also advances more slowly; the speed of the front decreases with time and is closer to <math> u_f = c_0 </math> than to <math> u_f = 2 c_0 </math>. The reason for this difference is the neglect of frictional effects that are important in the thin fluid layer near the front.<br />
<br />
<br />
[[image:FrictionlessDamBreakFlow4.png|thumb|center|900px|Box 1. Derivation of the solution for frictionless dam break flow.]]<br />
<br />
<br />
==Dam-break flow with friction==<br />
<br />
[[image:DamBreakWaveProfiles.jpg|thumb|left|400px|Fig. 4. Wave profile after dam break. The red curve corresponds to the frictionless solution Eq. 1. The blue band represents data from different laboratory experiments performed at times <math>\small t \sim (40-80) \, \sqrt {h_0 / g}\normalsize </math> after removal of the dam <ref>Dressler, R. 1954. Comparison of theories and experiments for the hydraulic dam-break wave. Proc. Int. Assoc. Scientific Hydrology Assemblée Générale, Rome, Italy 3 (38)M 319–328</ref> <ref>Schoklitsch, A. 1917. Über Dambruchwellen. Kaiserliche Akademie der Wissenschaften, Wien, Mathematisch-Naturwissenschaftliche Klasse, Sitzungberichte IIa, 126: 1489–1514</ref><ref>Cavaillé,Y. 1965. Contribution à l’étude de l’écoulement variable accompagnant la vidange brusque d’une retenue. Publ. Scient. et Techn. du Ministère de l’Air, 410, Paris, France, 165</ref>. The frictionless solution only depends on <math>x/t</math>. Observed wave profiles also depend on time <math>t</math> because of the decreasing wave tip speed.]]<br />
<br />
<br />
When friction terms are included in the flow equations, there is no exact analytical solution. It is generally assumed that the frictionless flow equations are valid in a short period after dam break and for small values of <math>x / (c_0 t) </math>. In the front zone, where the water depth is small, the momentum balance is dominated by frictional momentum dissipation. The inertia terms <math>\partial u / \partial t + u \partial u / \partial x </math> in the momentum equation can be ignored, that is, the current in the front region is mainly determined by the balance of gravitational acceleration <math> g \partial h / \partial x </math> and shear stress <math>\tau</math>, the latter term being proportional to the square of the flow velocity<ref>Dressler, R.F. 1952. Hydraulic resistance effect upon the dambreak functions. J. Res. Natl. Bureau of Standards, 49(3): 217–225</ref><ref>Whitham, G.B. 1955. The effects of hydraulic resistance in the dam-break problem. Proc. Roy. Soc. of London, Serie A, 227: 399–407</ref><ref>Hogg, A.J. and Pritchard, D. 2004. The effects of hydraulic resistance on dam-break and other shallow inertial flows. J. Fluid Mech. 501: 179–212</ref><ref name=C09>Chanson, H. 2009. Application of the method of characteristics to the dam break wave problem. Journal of Hydraulic Research 47: 41–49</ref>. With such models the shape of the wave front is given by <math>h(s) \propto s^n, \; n=1/2</math>, where <math>s</math> is the distance measured from the wave front. The wave front speed <math>u_f</math> decreases with time. At large times <math>t>>t_{\infty}</math>, the wave front speed varies approximately as <math>u_f \approx c_0 \sqrt{t_{\infty}/t}</math> <ref name=C09></ref>. Here, <math>t_{\infty} = \sqrt{h_0/g}/(3 c_D)</math> and <math>c_D</math> is the friction coefficient (value in the range <math>\approx (1-5)\, 10^{-3}</math>). A more elaborate model of the frictional boundary layer near the wave front was studied by Nielsen (2018) <ref name=PN>Nielsen, P. 2018 Bed shear stress, surface shape and velocity field near the tips of dam-breaks, tsunami and wave runup velocity. Coastal Engineering 138: 126–131</ref>. According to this model, the wavefront is even more blunt, corresponding to <math> n = 1/4 </math>, which agrees well with laboratory experiments. This model also reveals a strong downward velocity component at the wavefront, which can contribute to the dislodging of particles from the sediment bed <ref name = PN> </ref>. This may explain the high near-bed of suspended concentrations associated with propagating surges observed in the field<ref>Khezri, N. and Chanson, H. 2012. Inception of bed load motion beneath a bore. Geomorphology 153: 39–47</ref>, see also the article [[Tidal bore dynamics]]. <br />
<br />
<br />
For situations that can be schematically represented by simple geometries, parametric models have been developed based on data for a large number of previous dam breaks<ref> Wang, B., Chen, Y., Wu, C., Peng, Y., Song, J., Liu, W. and Liu, X. 2018. Empirical and semi-analytical models for predicting peak outflows caused by embankment dam failures. Journal of Hydrology 562: 692–702</ref>. <br />
<br />
<br />
==Numerical models==<br />
<br />
The analytical methods for describing dam-break flow provide a qualitative picture and some first-order estimates for the wave profile and wave speed. They may only be used in situations that can be represented schematically by a simple prismatic channel. In most actual field situations, the dam-break flow must be modeled numerically. Detailed simulation of the forward and backward wave fronts requires 3D models of the Boussinesq type, taking into account vertical fluid accelerations<ref>Castro-Orgaz, O. and Chanson, H. 2017. Ritter’s dry-bed dam-break flows: positive and negative wave dynamics. Environ Fluid Mech (2017) 17:665–694</ref>. To correctly model the strong temporal and spatial gradients of the surging wave, a fine computational grid is required, with resulting long computer times. <br />
<br />
<br />
<br />
==References==<br />
<references/></div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Testpage1&diff=76310Testpage12019-12-31T16:06:27Z<p>Dronkers J: </p>
<hr />
<div>=Dam break flow=<br />
<br />
<br />
==Introduction==<br />
<br />
[[image:Dijkdoorbraak1953.png|thumb|left|300px|Fig. 1. Sea dikes protecting low-lying polders in the Netherlands were breached during the extreme storm surge of 31 January 1953.]] <br />
<br />
<br />
<br />
<br />
<br />
Dam failure can lead to catastrophic situations. Most dam break tragedies are known for dam collapse in mountainous rivers. The failure of sea dikes can also cause major disasters, although the level difference is not that great. A dramatic example is the failure of more than fifty sea dikes in the Netherlands during the extreme storm surge of 1953, see figure 1. Many of these dikes protected land lying below the average sea level, while the storm surge level exceeded more than five meters. Rapid flooding killed many people who were unable to flee to safe places in time. This article does not discuss the causes of dam failure, but the resulting tidal wave.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
[[image:DamBreakFlowPrinciple.jpg|thumb|center|600px|Fig. 2. Left panel: Schematic representation of water retention behind a dam. Right panel: Positive downstream and negative upstream surges following instantaneous dam removal.]]<br />
<br />
<br />
The consequences of dam failure have been studied for more than a century. It nevertheless remains a challenging topic due to the high non-linearity of the flood wave propagation. The problem can be tackled with numerical models, but rough estimates and insight into the tidal wave dynamics can be obtained with analytical solution methods.<br />
<br />
<br />
==Frictionless dam-break flow: analytical solution==<br />
<br />
Analytical solutions relate to idealized situations as depicted in Fig. 2. The initial situation consists of an infinite reservoir with a water level that is <math> h_0 </math> higher than the horizontal ground level downstream of the dam. Dam break is simulated by instantaneous removal of the dam. This causes a positive surge in the positive <math> x </math>-direction and a negative surge in the negative <math> x </math>-direction. The floor is dry in front of the positive surge and the body of water behind the negative surge is undisturbed: water level <math> h_0 </math> and current speed <math> u = 0 </math>.<br />
<br />
[[image:SouthForkDamFailure1889.jpg|thumb|left|300px|Fig. 3. The earth-filled South Fork Dam on Lake Conemaugh (Pennsylvania, US) collapsed in 1889, killing 2,209 people in downstream villages.]]<br />
<br />
<br />
<br />
<br />
<br />
<br />
The study of the dam break-flow was initiated by several dam failures in the 19th century, in particular the breach of the South Fork Dam in Pennsylvania (USA) in 1889, Fig. 3. Three years later Ritter <ref> Ritter, A. 1892. Die Fortpflanzung der Wasserwellen. Zeitschrift des Vereines Deutscher Ingenieure 36: 947-954 </ref> published an exact analytical solution for dam-break flow by assuming that frictional effects can be ignored. The derivation is given in box 1. According to this solution, the tip of the positive surge advances at high speed (supercritical flow) given by <math> u_f = 2 c_0</math>, where <math>c_0 = \sqrt {gh_0}</math> and <math> g </math> is the gravitational acceleration. The shape of the positive and negative wave is a concave-up parabola,<br />
<math>h(x,t)= h_0, \; x/t<-c_0; \quad h(x,t)= \Large\frac{h_0}{9}\normalsize \; (2 - \Large\frac{x}{c_0 t}\normalsize) , \, -c_0<x/t<2c_0; \quad h(x,t)= 0, \, x/t>2c_0 , \qquad (1)</math><br />
<br />
see Fig. 4. The same figure also shows the shape of the dam break wave that was observed in laboratory experiments. For small values of <math> x / t </math>, the frictionless solution corresponds fairly well with the observations. However, the front zone is different: the shape is a bull nose, rather than a sharp edge. The front also advances more slowly; the speed of the front decreases with time and is closer to <math> u_f = c_0 </math> than to <math> u_f = 2 c_0 </math>. The reason for this difference is the neglect of frictional effects that are important in the thin fluid layer near the front.<br />
<br />
<br />
[[image:FrictionlessDamBreakFlow2.png|thumb|center|900px|Box 1. Derivation of the solution for frictionless dam break flow.]]<br />
<br />
<br />
==Dam-break flow with friction==<br />
<br />
[[image:DamBreakWaveProfiles.jpg|thumb|left|400px|Fig. 4. Wave profile after dam break. The red curve corresponds to the frictionless solution Eq. 1. The blue band represents data from different laboratory experiments performed at times <math>\small t \sim (40-80) \, \sqrt {h_0 / g}\normalsize </math> after removal of the dam <ref>Dressler, R. 1954. Comparison of theories and experiments for the hydraulic dam-break wave. Proc. Int. Assoc. Scientific Hydrology Assemblée Générale, Rome, Italy 3 (38)M 319–328</ref> <ref>Schoklitsch, A. 1917. Über Dambruchwellen. Kaiserliche Akademie der Wissenschaften, Wien, Mathematisch-Naturwissenschaftliche Klasse, Sitzungberichte IIa, 126: 1489–1514</ref><ref>Cavaillé,Y. 1965. Contribution à l’étude de l’écoulement variable accompagnant la vidange brusque d’une retenue. Publ. Scient. et Techn. du Ministère de l’Air, 410, Paris, France, 165</ref>. The frictionless solution only depends on <math>x/t</math>. Observed wave profiles also depend on time <math>t</math> because of the decreasing wave tip speed.]]<br />
<br />
<br />
When friction terms are included in the flow equations, there is no exact analytical solution. It is generally assumed that the frictionless flow equations are valid in a short period after dam break and for small values of <math>x / (c_0 t) </math>. In the front zone, where the water depth is small, the momentum balance is dominated by frictional momentum dissipation. The inertia terms <math>\partial u / \partial t + u \partial u / \partial x </math> in the momentum equation can be ignored, that is, the current in the front region is mainly determined by the balance of gravitational acceleration <math> g \partial h / \partial x </math> and shear stress <math>\tau</math>, the latter term being proportional to the square of the flow velocity<ref>Dressler, R.F. 1952. Hydraulic resistance effect upon the dambreak functions. J. Res. Natl. Bureau of Standards, 49(3): 217–225</ref><ref>Whitham, G.B. 1955. The effects of hydraulic resistance in the dam-break problem. Proc. Roy. Soc. of London, Serie A, 227: 399–407</ref><ref>Hogg, A.J. and Pritchard, D. 2004. The effects of hydraulic resistance on dam-break and other shallow inertial flows. J. Fluid Mech. 501: 179–212</ref><ref name=C09>Chanson, H. 2009. Application of the method of characteristics to the dam break wave problem. Journal of Hydraulic Research 47: 41–49</ref>. With such models the shape of the wave front is given by <math>h(s) \propto s^n, \; n=1/2</math>, where <math>s</math> is the distance measured from the wave front. The wave front speed <math>u_f</math> decreases with time. At large times <math>t>>t_{\infty}</math>, the wave front speed varies approximately as <math>u_f \approx c_0 \sqrt{t_{\infty}/t}</math> <ref name=C09></ref>. Here, <math>t_{\infty} = \sqrt{h_0/g}/(3 c_D)</math> and <math>c_D</math> is the friction coefficient (value in the range <math>\approx (1-5)\, 10^{-3}</math>). A more elaborate model of the frictional boundary layer near the wave front was studied by Nielsen (2018) <ref name=PN>Nielsen, P. 2018 Bed shear stress, surface shape and velocity field near the tips of dam-breaks, tsunami and wave runup velocity. Coastal Engineering 138: 126–131</ref>. According to this model, the wavefront is even more blunt, corresponding to <math> n = 1/4 </math>, which agrees well with laboratory experiments. This model also reveals a strong downward velocity component at the wavefront, which can contribute to the dislodging of particles from the sediment bed <ref name = PN> </ref>. This may explain the high near-bed of suspended concentrations associated with propagating surges observed in the field<ref>Khezri, N. and Chanson, H. 2012. Inception of bed load motion beneath a bore. Geomorphology 153: 39–47</ref>, see also the article [[Tidal bore dynamics]]. <br />
<br />
<br />
For situations that can be schematically represented by simple geometries, parametric models have been developed based on data for a large number of previous dam breaks<ref> Wang, B., Chen, Y., Wu, C., Peng, Y., Song, J., Liu, W. and Liu, X. 2018. Empirical and semi-analytical models for predicting peak outflows caused by embankment dam failures. Journal of Hydrology 562: 692–702</ref>. <br />
<br />
<br />
==Numerical models==<br />
<br />
The analytical methods for describing dam-break flow provide a qualitative picture and some first-order estimates for the wave profile and wave speed. They may only be used in situations that can be represented schematically by a simple prismatic channel. In most actual field situations, the dam-break flow must be modeled numerically. Detailed simulation of the forward and backward wave fronts requires 3D models of the Boussinesq type, taking into account vertical fluid accelerations<ref>Castro-Orgaz, O. and Chanson, H. 2017. Ritter’s dry-bed dam-break flows: positive and negative wave dynamics. Environ Fluid Mech (2017) 17:665–694</ref>. To correctly model the strong temporal and spatial gradients of the surging wave, a fine computational grid is required, with resulting long computer times. <br />
<br />
<br />
<br />
==References==<br />
<references/></div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Testpage1&diff=76307Testpage12019-12-29T15:43:49Z<p>Dronkers J: </p>
<hr />
<div>=Dam break flow=<br />
<br />
<br />
==Introduction==<br />
<br />
[[image:Dijkdoorbraak1953.png|thumb|left|300px|Fig. 1. Sea dikes protecting low-lying polders in the Netherlands were breached during the extreme storm surge of 31 January 1953.]] <br />
<br />
<br />
<br />
<br />
<br />
Dam failure can lead to catastrophic situations. Most dam break tragedies are known for dam collapse in mountainous rivers. The failure of sea dikes can also cause major disasters, although the level difference is not that great. A dramatic example is the failure of more than fifty sea dikes in the Netherlands during the extreme storm surge of 1953, see figure 1. Many of these dikes protected land lying below the average sea level, while the storm surge level exceeded more than five meters. Rapid flooding killed many people who were unable to flee to safe places in time. This article does not discuss the causes of dam failure, but the resulting tidal wave.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
[[image:DamBreakFlowPrinciple.jpg|thumb|center|600px|Fig. 2. Left panel: Schematic representation of water retention behind a dam. Right panel: Positive downstream and negative upstream surges following instantaneous dam removal.]]<br />
<br />
<br />
The consequences of dam failure have been studied for more than a century. It nevertheless remains a challenging topic due to the high non-linearity of the flood wave propagation. The problem can be tackled with numerical models, but rough estimates and insight into the tidal wave dynamics can be obtained with analytical solution methods.<br />
<br />
<br />
==Frictionless dam-break flow: analytical solution==<br />
<br />
Analytical solutions relate to idealized situations as depicted in Fig. 2. The initial situation consists of an infinite reservoir with a water level that is <math> h_0 </math> higher than the horizontal ground level downstream of the dam. Dam break is simulated by instantaneous removal of the dam. This causes a positive surge in the positive <math> x </math>-direction and a negative surge in the negative <math> x </math>-direction. The floor is dry in front of the positive surge and the body of water behind the negative surge is undisturbed: water level <math> h_0 </math> and current speed <math> u = 0 </math>.<br />
<br />
[[image:SouthForkDamFailure1889.jpg|thumb|left|300px|Fig. 3. The earth-filled South Fork Dam on Lake Conemaugh (Pennsylvania, US) collapsed in 1889, killing 2,209 people in downstream villages.]]<br />
<br />
<br />
<br />
<br />
<br />
<br />
The study of the dam break-flow was initiated by several dam failures in the 19th century, in particular the breach of the South Fork Dam in Pennsylvania (USA) in 1889, Fig. 3. Three years later Ritter <ref> Ritter, A. 1892. Die Fortpflanzung der Wasserwellen. Zeitschrift des Vereines Deutscher Ingenieure 36: 947-954 </ref> published an exact analytical solution for dam-break flow by assuming that frictional effects can be ignored. The derivation is given in box 1. According to this solution, the tip of the positive surge advances at high speed (supercritical flow) given by <math> u = 2 c_0</math>, where <math>c_0 = \sqrt {gh_0}</math> and <math> g </math> is the gravitational acceleration. The shape of the positive and negative wave is a concave-up parabola,<br />
<math>h(x,t)= h_0, \; x/t<-c_0; \quad h(x,t)= \Large\frac{h_0}{9}\normalsize \; (2 - \Large\frac{x}{c_0 t}\normalsize) , \, -c_0<x/t<2c_0; \quad h(x,t)= 0, \, x/t>2c_0 , \qquad (1)</math><br />
<br />
see Fig. 4. The same figure also shows the shape of the dam break wave that was observed in laboratory experiments. For small values of <math> x / t </math>, the frictionless solution corresponds fairly well with the observations. However, the front zone is different: the shape is a bull nose, rather than a sharp edge. The front also advances more slowly; the speed of the front decreases with time and is closer to <math> u = c_0 </math> than to <math> u = 2 c_0 </math>. The reason for this difference is the neglect of frictional effects that are important in the thin fluid layer near the front.<br />
<br />
<br />
[[image:FrictionlessDamBreakFlow.png|thumb|center|900px|Box 1. Derivation of the solution for frictionless dam break flow.]]<br />
<br />
<br />
==Dam-break flow with friction==<br />
<br />
[[image:DamBreakWaveProfiles.jpg|thumb|left|400px|Fig. 4. Wave profile after dam break. The red curve corresponds to the frictionless solution Eq. 1. The blue band represents data from different laboratory experiments performed at times <math>\small t \sim (40-80) \, \sqrt {h_0 / g}\normalsize </math> after removal of the dam <ref>Dressler, R. 1954. Comparison of theories and experiments for the hydraulic dam-break wave. Proc. Int. Assoc. Scientific Hydrology Assemblée Générale, Rome, Italy 3 (38)M 319–328</ref> <ref>Schoklitsch, A. 1917. Über Dambruchwellen. Kaiserliche Akademie der Wissenschaften, Wien, Mathematisch-Naturwissenschaftliche Klasse, Sitzungberichte IIa, 126: 1489–1514</ref><ref>Cavaillé,Y. 1965. Contribution à l’étude de l’écoulement variable accompagnant la vidange brusque d’une retenue. Publ. Scient. et Techn. du Ministère de l’Air, 410, Paris, France, 165</ref>. The frictionless solution only depends on <math>x/t</math>. Observed wave profiles also depend on time <math>t</math> because of the decreasing wave tip speed.]]<br />
<br />
<br />
When friction terms are included in the flow equations, there is no exact analytical solution. In this case, it is generally assumed that the frictionless flow equations are valid for small values of <math>x / (c_0 t) </math>, while in the front zone the inertia terms <math>\partial u / \partial t + u \partial u / \partial x </math> in the momentum equation can be ignored, that is, the current in the front region is mainly determined by the balance of gravitational acceleration <math> g \partial h / \partial x </math> and shear stress <math>\tau</math>, the latter term being proportional to the square of the flow velocity<ref>Dressler, R.F. 1952. Hydraulic resistance effect upon the dambreak functions. J. Res. Natl. Bureau of Standards, 49(3): 217–225</ref><ref>Whitham, G.B. 1955. The effects of hydraulic resistance in the dam-break problem. Proc. Roy. Soc. of London, Serie A, 227: 399–407</ref><ref>Hogg, A.J. and Pritchard, D. 2004. The effects of hydraulic resistance on dam-break and other shallow inertial flows. J. Fluid Mech. 501: 179–212</ref><ref name=C09>Chanson, H. 2009. Application of the method of characteristics to the dam break wave problem. Journal of Hydraulic Research 47: 41–49</ref>. With such models the shape of the wave front is given by <math>h(s) \propto s^n, \; n=1/2</math>, where <math>s</math> is the distance measured from the wave front. The wave front speed <math>u_f</math> decreases with time as <math>u_f \approx c_0 \sqrt{t_{\infty}/t}</math> at large times: <math>t>>t_{\infty}</math> <ref name=C09></ref>, where <math>t_{\infty} = \sqrt{h_0/g}/(3 c_D)</math> and <math>c_D</math> is the friction coefficient (value in the range <math>\approx (1-5)\, 10^{-3}</math>). A more elaborate model of the frictional boundary layer near the wave front was studied by Nielsen (2018) <ref name=PN>Nielsen, P. 2018 Bed shear stress, surface shape and velocity field near the tips of dam-breaks, tsunami and wave runup velocity. Coastal Engineering 138: 126–131</ref>. According to this model, the wavefront is even more blunt, corresponding to <math> n = 1/4 </math>, which agrees well with laboratory experiments. This model also reveals a strong downward velocity component at the wavefront, which can contribute to the dislodging of particles from the sediment bed <ref name = PN> </ref>. This may explain the high near-bed of suspended concentrations associated with propagating surges observed in the field<ref>Khezri, N. and Chanson, H. 2012. Inception of bed load motion beneath a bore. Geomorphology 153: 39–47</ref>, see also the article [[Tidal bore dynamics]]. <br />
<br />
<br />
For situations that can be schematically represented by simple geometries, parametric models have been developed based on data for a large number of previous dam breaks<ref> Wang, B., Chen, Y., Wu, C., Peng, Y., Song, J., Liu, W. and Liu, X. 2018. Empirical and semi-analytical models for predicting peak outflows caused by embankment dam failures. Journal of Hydrology 562: 692–702</ref>. <br />
<br />
<br />
==Numerical models==<br />
<br />
The analytical methods for describing dam-break flow provide a qualitative picture and some first-order estimates for the wave profile and wave speed. They may only be used in situations that can be represented schematically by a simple prismatic channel. In most actual field situations, the dam-break flow must be modeled numerically. Detailed simulation of the forward and backward wave fronts requires 3D models of the Boussinesq type, taking into account vertical fluid accelerations<ref>Castro-Orgaz, O. and Chanson, H. 2017. Ritter’s dry-bed dam-break flows: positive and negative wave dynamics. Environ Fluid Mech (2017) 17:665–694</ref>. To correctly model the strong temporal and spatial gradients of the surging wave, a fine computational grid is required, with resulting long computer times. <br />
<br />
<br />
<br />
==References==<br />
<references/></div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=File:SouthForkDamFailure1889.jpg&diff=76304File:SouthForkDamFailure1889.jpg2019-12-29T14:22:27Z<p>Dronkers J: Breach of the earth-filled South Fork Dam on Lake Conemaugh (Pennsylvania, US) in 1889.</p>
<hr />
<div>== Summary ==<br />
Breach of the earth-filled South Fork Dam on Lake Conemaugh (Pennsylvania, US) in 1889.</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=File:Dijkdoorbraak1953.png&diff=76303File:Dijkdoorbraak1953.png2019-12-29T14:20:53Z<p>Dronkers J: Sea dikes protecting low-lying polders in the Netherlands were breached during the extreme storm surge of 31 January 1953.</p>
<hr />
<div>== Summary ==<br />
Sea dikes protecting low-lying polders in the Netherlands were breached during the extreme storm surge of 31 January 1953.</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=File:DamBreakWaveProfiles.jpg&diff=76302File:DamBreakWaveProfiles.jpg2019-12-29T14:18:58Z<p>Dronkers J: Wave profile after dam break. Red line: frictionless solution. Blue band: experimental lab data.</p>
<hr />
<div>== Summary ==<br />
Wave profile after dam break. Red line: frictionless solution. Blue band: experimental lab data.</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=File:DamBreakFlowPrinciple.jpg&diff=76301File:DamBreakFlowPrinciple.jpg2019-12-29T14:17:01Z<p>Dronkers J: Left panel: Schematic representation of water retention behind a dam. Right panel: Positive downstream and negative upstream surges following instantaneous dam removal.</p>
<hr />
<div>== Summary ==<br />
Left panel: Schematic representation of water retention behind a dam. Right panel: Positive downstream and negative upstream surges following instantaneous dam removal.</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Tidal_asymmetry_and_tidal_basin_morphodynamics&diff=76284Tidal asymmetry and tidal basin morphodynamics2019-12-17T14:29:13Z<p>Dronkers J: </p>
<hr />
<div><br />
This article describes the physical processes responsible for tidal wave deformation in shallow coastal inlet systems – tidal lagoons and estuaries. A qualitative discussion is given of the mutual interaction between tidal asymmetry generation and morphological development of these systems, which is generally referred to by the term ''self-organizing morphodynamics''. This article is largely based on the book ''Dynamics of Coastal Systems'' <ref name=Dr>Dronkers, J. 2017. Dynamics of Coastal Systems. World Scientific Publ. Co, Singapore, 740 pp.</ref>. <br />
<br />
==Tidal wave deformation in shallow water==<br />
<br />
Tides result from the response of the ocean water bodies to the attractive gravitational forces by sun and moon. Tidal motion in the oceans can be described by a limited number of sinusoidal components, because earth's rotation and the relative movements of earth, sun and moon have a cyclical character, see the article [[Ocean and shelf tides]]. The semidiurnal lunar tide (M2) is usually the dominant component, in which case the ocean tide can be described fairly accurately with a single sine function.<br />
<br />
Ocean tidal waves are distorted when they propagate into shallow coastal waters. Here the term tidal wave distortion is to be understood as a systematic (long-term averaged) difference between the periods of rising and falling tide, also called tidal asymmetry. We will use the term positive duration asymmetry for tides with a longer fall and shorter rise and negative duration asymmetry for tides with a shorter fall and longer rise. Nonlinear hydrodynamic processes that are insignificant in the deep ocean become important when the tidal range is larger than a small fraction of the mean water depth. In the following we shortly review the major nonlinear processes involved in initiating shallow-water tidal distortion. <br />
<br />
However, it must be noted before that linear ocean tides are not fully symmetric, due to the superposition of certain tidal components with mutually related frequencies (for example, the sum of the frequencies of the K1 and O1 tides is equal to the frequency of the M2 tide). Although this was known for a long time (Doodson, 1921)<ref> Doodson, A.T. 1921. The harmonic development of the tide-generating potential. Proc.R.Soc.London, Ser.A 100: 305-329</ref>, it has received renewed attention more recently due to the observations and analyses of Hoitink et al. (2003)<ref> Hoitink, A.F.J., Hoekstra, P. and van Mare, D.S. 2003. Flow asymmetry associated with astronomical tides: Implications for residual transport of sediment. J.Geophys.Res. 108: 13-1 - 13-8</ref> and several other studies since (Nidzieko, 2010<ref>Nidzieko, J. 2010. Tidal asymmetry in estuaries with mixed semidiurnal/diurnal tides. J. Geophysical Research 115, C08006, doi:10.1029/2009JC005864</ref>; Zhang, 2018 <ref>Zhang, W., Cao, Y., Zhu, Y., Zheng, J., Ji, X., Xu, Y., Wu, Y. and Hoitink, A.F.J. 2018. Unravelling the causes of tidal asymmetry in deltas. Journal of Hydrology 564: 588–604</ref>). A world map showing ocean regions with [[Ocean and shelf tides#Asymmetric ocean tides|asymmetric tides]] was published by Song et al. (2011<ref> Song, D., X. H. Wang, A. E. Kiss, and Bao, X. 2011. The contribution to tidal asymmetry by different combinations of tidal constituents. J. Geophys. Res., 116, C12007</ref>), based on tidal constants derived from the TPXO7-ATLAS (http://volkov.oce.orst.edu/tides/atlas.html). Asymmetric tides (with either positive or negative duration asymmetry) occur mainly in regions where tides have a mixed character, with comparable magnitudes of diurnal and semidiurnal tidal components. <br />
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Although the asymmetry of ocean tides can be significant, tidal asymmetry can become much stronger due to the generation of shallow-water overtides in shallow coastal areas with a large semidiurnal tidal range (dominated by M2). The distortion of the tide can be so strong that the durations of rising tide and falling tide become very different and that a large difference arises between the peak flow velocities of flood and ebb. Often the duration of rising tide is much shorter than the duration of falling tide. This is illustrated in Fig. 1 for the [[Morphology of estuaries#Hooghly estuary|Hooghly estuary]]. In the most extreme case, the duration of tidal rise becomes so short that a hydraulic jump develops at the front of the tidal wave. The front of the tidal wave appears as a propagating wall of water, a so-called tidal bore, as explained in the article [[Tidal bore dynamics]]. <br />
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[[Image:HooghlyTidalWaveDeformation.jpg|center|700px|thumb|Figure 1: Tide curves in the Hooghly estuary observed during a high springtide (19/9/2009) at different tide gauges along the estuary. Data from Banerjee et al. (2015)<ref>Banerjee, A.P., Dutta, S. and Majumdar, A. 2015. Quest for the determination of environmental flow assessment for hilsa fish of the Hooghly estuary by hydraulic rating method. ARPN Journal of Engineering and Applied Sciences 10: 7885-7899</ref>]]<br />
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We focus here on asymmetry generated by the interaction of tides with topographic characteristics. Most studies of overtide generation consider estuaries and tidal rivers with simple one-dimensional geometries. In these studies, the influence of channel curvature, secondary channels or local channel constrictions on tidal asymmetry are ignored. Asymmetries related to density gradients or wind-driven currents are also left out of consideration. <br />
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==Tidal wave deformation in the absence of friction==<br />
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The distortion of the tide described above is related to a difference in propagation speed of the high-water crest of the tidal wave and the low-water trough. This difference already occurs when the water depth below the wave crest is slightly greater than the water depth below the wave trough. This can be easily demonstrated for a tidal wave that propagates in <math>x</math>-direction with time <math>t</math> in deep water with little loss of friction. The most simple geometry is an infinite prismatic channel. The mean (tide-averaged) channel depth is called <math>h</math> (constant), the tidal elevation is called <math>\zeta(x,t)</math>, the total instantaneous water depth <math>D(x,t)=h+\zeta(x,t)</math> and the cross-sectionally averaged velocity <math>u(x,t)</math>. <br />
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In the absence of friction, the tidal equations for mass and momentum read:<br />
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<math>\Large\frac{\partial \zeta}{\partial t}\normalsize +\Large\frac{\partial((h+\zeta)u)}{\partial x}\normalsize=0 ; \qquad \Large\frac{\partial u}{\partial t}\normalsize + u \Large\frac{\partial u}{\partial x} \normalsize + g \Large\frac{\partial \zeta}{\partial x}\normalsize = 0 , \qquad (1)</math><br />
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where <math>g</math> is the gravitational acceleration. Overtides are due to the nonlinear terms <math>\partial(\zeta u) / \partial x </math> and <math> u \partial u / \partial x</math>. The quadratic nature of these terms implies that the first and most important overtide (M4) has twice the frequency of the M2 tide. <br />
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The tidal equations (1) can be cast in the form of two characteristic equations<br />
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<math>\Large\frac{d}{dt}\normalsize[u(x(t),t) +2c(x(t),t)] = 0, \; \Large\frac{d x(t)}{dt}\normalsize = u(x(t),t) + c(x(t),t) ; \qquad \Large\frac{d}{dt}\normalsize[u(x(t),t) - 2c(x(t),t)] = 0, \; \Large\frac{d x(t)}{dt}\normalsize = u(x(t),t) - c(x(t),t) , \qquad (2)</math><br />
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where <math>c = \sqrt{gD}</math>. The first equation represents a wave propagating in positive <math>x</math>-direction and the second a wave propagating in negative <math>x</math>-direction. The wave crest propagating in positive <math>x</math>-direction thus moves with speed<br />
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<math>c = u_{crest} + \sqrt{g(h+a)} , \qquad (3) </math><br />
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where <math>a</math> is the wave crest height. If we assume <math>a <<h</math>, then the velocity at the wave crest <math>u_{crest}</math> can be derived from the linearized equations (1) (i.e., replacing <math>\partial(Du)/\partial x</math> by <math>\partial(hu)/\partial x</math> and neglecting the term <math>u \partial u / \partial x</math>), with the result <math>u_{crest} = (a/h) \sqrt{gh}</math>. Substitution in Eq. (3) we find<br />
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<math>c \approx \Large\frac{a}{h}\normalsize \sqrt{gh} + \sqrt{g(h+a)} \approx \sqrt{gh} (1 + \Large\frac{3a}{2h}\normalsize) . \quad \quad (4)</math><br />
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[[Image:PropagatingWaveDeformation.jpg|right|400px|thumb|Figure 2: Deformation of a frictionless propagating wave. The blue curve is the sinusoidal tidal wave with amplitude <math>a</math> of 2 m, at <math>\small x=0</math>, <math>\small\zeta(x=0,t) = a \cos \omega t</math>. The red curve is the distorted tidal wave after travelling a distance of <math>\small x=</math> 100 km without friction in a channel of 10 m mean depth, according to the second-order solution of Eqs. (1) and (2) for <math>a/h<<1</math>, which is given by <math>\small \zeta(x,t) = \zeta^{(1)} + \zeta^{(2)} </math>, with <math>\small \zeta^{(1)} = a \cos(\omega t - kx)</math>, <math>\small\zeta^{(2)} = \large\frac{3 a^2}{4h} \small kx \sin(2 \omega t – 2kx) </math> (see appendix). The dotted red line is the M4 overtide <math>\small \zeta^{(2)} </math>. The red curve displays a shorter tidal rise and a longer tidal fall: the tidal wave crest has propagated faster than the tidal wave trough.]]<br />
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In the same way one finds for the propagation velocity of the low-water (LW) location <math>c^- \approx \sqrt{gh} (1 – \frac{3a}{2h})</math>. Another method to find this result is presented in the appendix. As HW propagates faster than LW, the tidal wave front will steepen progressively; the duration of rising tide shortens while the duration of falling tide is lengthened. This positive tidal asymmetry increases with the relative tidal amplitude <math>a/h</math> as a consequence of the nonlinear terms <math>\partial(\zeta u) / \partial x </math> and <math> u \partial u / \partial x</math> in the tidal equations. The resulting tidal distortion is illustrated in Fig. 2. Equation (4) suggests that after some time the high-water wave crest will overtake the low-water wave trough. However, this can only happen when the amplitude of the M4 overtide is of the same order of magnitude as the M2 tide, which violates the approximations used in Eq. (4).<br />
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The tidal equations for a prismatic channel do not well represent tidal propagation in estuaries because of neglect of the friction term. The equations (1,2) are more representative for the [[Coriolis and tidal motion in shelf seas|along-shore propagation of a tidal Kelvin wave]], far away from hard boundaries where the tidal wave can reflect or from hydrodynamic boundaries where the Kelvin wave meets other tidal wave systems. An increasing tidal asymmetry develops in situations where the coastal zone is shallow and the tidal amplitude is large. The increasing tidal asymmetry along the coast of Normandy (France) can be understood in this way (Fig. 3), as well as the increasing tidal asymmetry along the North Sea coast of Holland (see: [[Coriolis and tidal motion in shelf seas]]). The tidal wave that enters estuaries situated along such coasts (the Seine at Le Havre, for instance) exhibits already significant positive-duration tidal asymmetry.<br />
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[[Image:ChannelFrance.png|center|600px|thumb|Figure 4. Increasing positive asymmetry (<math>\Delta_{FR}</math> is the difference of the durations of tidal fall and tidal rise) of the tidal wave propagating along the coast of Normandy (France). Tide gauge data of 29 September 2015.]]<br />
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==Tidal wave deformation in the presence of friction and intertidal areas==<br />
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Tidal asymmetry develops during up-channel propagation into a shallow tidal basin. Pronounced tidal asymmetry (possibly leading to tidal bore formation) only occurs if during propagation a sufficiently large ratio <math>a/h</math> is maintained. In many cases this condition is not met, because the tidal amplitude decreases during propagation. The two main reasons for decrease of the tidal amplitude are: (1) tidal wave damping by friction and (2) lateral spreading of the flood tidal wave. These two nonlinear processes also influence the propagation of the high-water wave crest and the low-water wave trough. <br />
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We consider a tidal basin where the longitudinal tidal flow <math>u(x,t)</math> is confined in a single tidal channel with depth <math>D(x,t)</math> and width <math>B_C(x)</math>. Flood water can spread over intertidal areas; the width of the intertidal area <math>B_I(x,t)</math> is a function of the water level <math>\zeta(x,t)</math>. The tidal propagation in this basin can be described by the mass and momentum balance equations<br />
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<math>B \Large\frac{\partial \zeta}{\partial t}+\frac{\partial}{\partial x}\normalsize (B_C Du) = 0 , \quad \quad (5)</math><br />
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<math>\Large\frac{\partial u}{\partial t}\normalsize + u \Large\frac{\partial u}{\partial x} \normalsize + g \Large\frac{\partial \zeta}{\partial x}\normalsize + F = 0 , \quad \quad (6)</math><br />
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where <math>B= B_C+B_I </math> is the total surface width. The symbol <math>F</math> in Eq. (6) stands for the frictional momentum dissipation which is usually represented by a quadratic expression of the form <math>F= c_D \large\frac{|u|u}{D} </math>. Although it appears from detailed measurements that this expression is a rough approximation – the friction coefficient <math>c_D</math> is found to be variable both temporally and spatially (Lewis and Lewis, 1987<ref> Lewis, R. E., and Lewis, J. O. 1987. Shear-stress variations in an estuary. Estuarine Coastal Shelf Sci. 25: 621–635</ref>; Stacey and Ralston, 2005<ref name=SR> Stacey, M.T. and Ralston, D.K. 2005. The Scaling and Structure of the Estuarine Bottom Boundary Layer. J. Physical Oceanography 35: 55-71</ref>; Lefebvre et al., 2012<ref> Lefebvre, A., Ernstsen, V.B and Winter, C. 2012. Estimation of roughness lengths and flow separation over compound bedforms in a natural-tidal inlet. Continental Shelf Research 61–62: 98-111 </ref>) – we consider here a further approximation assuming that the quadratic dependence on <math>u</math> can be ignored: <math>F = r \large\frac{u}{D}</math>. Here, is <math>r</math> a constant friction coefficient with dimension [m/s] that relates momentum dissipation at the channel bed to the depth-averaged current velocity. Its value typically ranges between 0.001 - 0.004 m/s <ref name=Dr></ref>. The precise value of the friction coefficient for estuarine flow is generally not well known as it is influenced by many factors such as density stratification (lower friction), small bed forms (higher friction) and fluid mud layers (lower friction). The friction coefficient may even be different for ebb and flood because of differences in salinity stratification<ref name=SR></ref>. In most estuaries, the tidal discharge amplitude is much larger than the river discharge, which therefore does not strongly influence frictional dissipation in the absence of salinity stratification. In this case, the linearization of the friction term is a minor approximation compared to the uncertainty in the value of the friction coefficient.<br />
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[[Image:PrismaticTidalFlatChannelNEW.jpg|right|300px|thumb|Figure 4: Prismatic estuarine channel with tidal flats.]]<br />
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The tidal equations (5) and (6) are too complex for an analytic treatment in which tidal asymmetry is explicitly related to the nonlinear terms. An analytical solution of the tidal equations requires further approximations, by assuming that the contribution of nonlinear terms is relatively small and can be linearized (Lanzoni and Seminara, 1998<ref> Lanzoni, S. and Seminara, G. 1998. On tide propagation in convergent estuaries, J. Geophys. Res. 103: 30793–30812</ref>).<br />
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Therefore we consider a prismatic tidal channel with a uniform mean depth <math>h</math> much larger than the tidal amplitude <math>a</math>, such that the friction term can be approximated by<br />
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<math>F = r \Large\frac{u}{D}\normalsize =r \Large\frac{u(x,t)}{h+\zeta(x,t)}\normalsize \approx r\Large\frac{u(x,t)}{h}\normalsize (1 - \Large\frac{\zeta(x,t)}{h}\normalsize) . \quad \quad (7)</math> <br />
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We further assume that the intertidal storage width <math>B_I</math> is much smaller than the channel width <math>B_C</math> and that it increases linearly with the water level <math>\zeta(x,t)</math> (see Fig. 4):<br />
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<math>B_I = \Delta b (1 + \Large\frac{\zeta(x,t)}{h}\normalsize), \quad <B>=B_C+\Delta b . \quad \quad (8)</math> <br />
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In shallow estuaries (<math>h \le 5 m</math>) with strong tides, the nondimensional friction coefficient <math>r / (h \omega)</math> is substantially larger than 1 (the symbol <math>\omega</math> is the M2 tidal frequency). In this case the inertial terms <math>\partial u / \partial x </math> and <math> u \partial u / \partial x</math> are much smaller than the friction term <math>F</math>.<br />
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In prismatic well-mixed estuaries, where salinity stratification can be ignored and where frictional effects are much stronger than inertial effects, the one-dimensional cross-section-averaged tidal equations (5) and (6) for small values of <math>a/h</math> can be simplified to <br />
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<math><B> \Large \frac{\partial \zeta}{\partial t} \normalsize + h B_C \Large \frac{\partial u}{\partial x}\normalsize + \Delta b \Large \frac{\zeta}{a} \frac{\partial \zeta}{\partial t} \normalsize + B_C \Large \frac{\partial (\zeta u)}{\partial x}\normalsize =0 , \quad \quad (9)</math><br />
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<math>g\Large \frac{\partial \zeta}{\partial x}\normalsize + r \Large \frac{u}{h}\normalsize – r \Large \frac{u \zeta}{h^2}\normalsize =0 . \quad \quad (10)</math><br />
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In such friction-dominated estuaries the tide does not travel as a propagating wave, but rather advances into the estuary through a diffusion-type process, as shown by Eq. (B5) and described by Blondeaux (1978) for the Saint Lawrence Estuary <ref name=LB> LeBlond, P. 1978. On tidal propagation in shallow rivers, J. Geophys. Res., 83: 4717–4721</ref>. The tidal wave crest does not coincide with the time of high water, but lags behind. The same applies to low water.<br />
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The nonlinear terms in the tidal equations are much smaller than the linear terms if <math>\Delta b << B_C</math> and <math>a/h << 1</math>. In this case a first order solution <math>\zeta^{(1)}</math> can be found by substituting the solution of the linear equations in the nonlinear terms. The nonlinear terms then generate a small M4 tidal component <math>\zeta^{(2)}</math>, which affects the duration of tidal rise and tidal fall. This is because the propagation speed <math>c^+</math> of the high-water wave crest differs from the propagation speed <math>c^-</math> of the low-water wave trough (see appendix):<br />
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<math>c^{\pm} \approx [1 \pm (2 - \sqrt{2}) \Large\frac{a}{h}\normalsize \mp \Large\frac{\Delta b}{2B_C}\normalsize ] \; \sqrt{gh} \; \sqrt{ \Large\frac{2 \omega h}{r} \frac{B_C}{<B>}\normalsize} . \quad \quad (11) </math> <br />
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where <math>\omega</math> is the M2 radial frequency. <br />
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This expression exhibits the effect of other nonlinearities in tidal propagation than those considered in the example of the prismatic channel: the effect of intertidal areas in Eq. (9) and the effect of depth dependence of the friction term in Eq. (10). The nonlinearity in the friction term Eq. (7) implies less friction in the period around HW compared to the period around LW and a corresponding increase of the HW propagation speed compared to the LW propagation, yielding positive tidal asymmetry. The nonlinearity related to the width increase with rising water level represented by the third term in Eq. (9) implies a decrease of the HW propagation velocity compared to the LW propagation, yielding negative tidal asymmetry (Speer and Aubrey, 1985<ref> Speer, P.E. and Aubrey, D.G. 1985. A study of non-linear tidal propagation in shallow inlet/estuarine systems. Part II: theory. Estuarine, Coastal Shelf Sci. 21: 207-224</ref>). This is because the HW crest of the tidal wave is delayed when propagating into the estuary by diversion of flood water over the intertidal area, while the LW wave trough remains confined within the narrower channel when propagating into the estuary. Hence, shallowness of the channel (large <math>a/h</math>) and large intertidal area (large <math>\Delta b/B_C</math>) have counteracting effects on tidal wave distortion.<br />
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==Morphology of shallow tidal basins with small river inflow==<br />
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In the foregoing it was shown that the tidal wave that enters a shallow prismatic channel is distorted due to the opposite effects of friction and intertidal areas on the up-channel propagation of HW on the one hand and LW on the other. In short tidal basins, these effects are partially offset by the reflected tidal wave at the landward basin boundary<ref name=Dr></ref>. However, in the case of strong friction, the reflected tidal wave is much smaller than the incoming tidal wave in a large part of the basin. In this part of the tidal basin the tidal velocity <math>u</math> is mainly determined by the water surface slope <math>\partial \zeta /\partial x</math>, according to Eq. 10. A short period of tidal rise compared to the period of tidal fall implies steeper water surface slopes during flood than during ebb. Hence, maximum flood velocities are higher than maximum ebb velocities in the absence of significant river inflow. <br />
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[[Image:EquilibriumTidalLagoonsNEW.jpg|right|500px|thumb|Figure 5: The relative tidal amplitude <math>a/h</math> versus the relative intertidal area <math>\Delta b/<B></math> for a large number of tidal basins with small (or without) river inflow. Many of these basins (but not all) are back-barrier tidal basins or tidal lagoons: basins that are semi-closed by a sand barrier at the entrance. The figure shows a positive correlation between <math>a/h</math> and <math>\Delta b/<B></math>. The correlation between these basin characteristics also depends on other parameters, in particular the tidal asymmetry already existing at the basin entrance, which is different for each basin. Therefore, one should not expect that all the point lie on a single line. Adapted from<ref name=Dr></ref>.]]<br />
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Because the transported sediment load increases more than linearly with the current velocity (see the articles [[Sand transport]] and [[Sediment transport formulas for the coastal environment]]), sediment fluxes during flood tide are higher than sediment fluxes during ebb tide. Flood-dominant tidal asymmetry thus produces a net import of sediment into the basin. Sediment infill could possibly go on until no tidal basin is left. This has happened in the past to some tidal basins, but many tidal basins without river inflow still survive. The reason is that flood dominance is neutralized by several processes. One of these processes is wave action, which can suspend large amounts of sediment in the HW period that are subsequently transported out of the basin by ebb currents<ref>Friedrichs, C.T. 2011. Tidal Flat Morphodynamics: A Synthesis. In: Treatise on Estuarine and Coastal Science, vol. 3, Estuarine and Coastal Geology and Geomorphology. Ed.:J. D. Hansom and B. W. Fleming, Elsevier, Amsterdam: 137-170</ref><ref> Desguée, R., Robin, N., Gluard, L., Monfort, O., Anthony, E.J., Levoy, F. 2011. Contribution of hydrodynamic conditions during shallow water stages to the sediment balance on a tidal flat: Mont-Saint-Michel bay, Normandy, France. Estuarine<br />
Coastal Shelf Sci. 94: 343–354</ref>. However, tidal basins do not depend only on wave action for their survival. One reason is the so-called Stokes transport, the water outflow compensating for the net influx due to greater mean water depth during flood than during ebb. Another reason is the reduction of tidal asymmetry due to the presence of intertidal areas as discussed in the previous section. During the development of intertidal areas by flood-dominant sediment transport, tidal asymmetry is weakened until the average sediment transport by flood currents has become comparable to the average transport by ebb currents. In order to neutralize flood dominance with increasing relative tidal amplitude <math>a/h</math>, the counteracting effect of intertidal areas should also increase. Fig. 5 shows that this is indeed the case for natural tidal basins with small (or without) river inflow: tidal basins with larger relative tidal amplitude have larger intertidal areas. One may thus conclude that self-organizing processes can produce a natural equilibrium morphology for tidal basins in a sedimentary environment without geological constraints<ref name=Dr></ref> <ref>Dronkers, J. 1998. Morphodynamics of the Dutch Delta. In: Physics of estuaries and coastal seas. Ed.: J.Dronkers and M.B.A.M. Scheffers, Balkema, Rotterdam: 297-304</ref> (see also the article [[Morphology of estuaries]]). <br />
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==Tidal wave deformation in a converging channel==<br />
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The influence of friction on tidal propagation increases with decreasing depth. The LW propagation is slowed down more strongly than the HW propagation, which results in a larger tidal asymmetry. However, the tidal amplitude is decreased by frictional damping. During the past century many estuaries have been deepened for navigational purposes and intertidal areas have been reclaimed. The effect of these interventions on tidal propagation is illustrated in Fig. 6 for the Seine estuary and tidal river system. The tide propagates now much faster into the estuary and the tidal amplitude is much larger, especially in the upstream river. The tide propagation speed has increased more for the low waters than for the high waters, although the propagation of the high waters also benefits of the reduction of the intertidal areas. In the past a high tidal bore developed each spring tide in the downstream river. After the interventions (especially the dredging of the mouth bar) it takes a much larger distance before the HW wave crest overtakes the LW wave trough. A small tidal bore now develops far upstream and only for very high tidal coefficients<ref> Bonneton, N., Bonneton, P., Parisot, J-P., Sottolichio, A. and Detandt G. 2012. Tidal bore and Mascaret - example of Garonne and Seine Rivers. Comptes Rendus Geosciences, 344, 508-515</ref>. <br />
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[[Image: SeineTidalDeformation.jpg|center|800px|thumb|Figure 6: Tidal wave distortion in the Seine estuary. The figures at the left show simultaneously recorded tide curves during springtide, for locations at various distances from the estuarine mouth. The images on the right show the morphology of the Seine estuary. The upper figures relate to the situation in the 19th century, when the morphology of the Seine estuary was almost in a natural state, with large shoals at the mouth (mouth bars) and an inner system with multiple channels and extensive intertidal areas. The 1876 tide curves (Comoy, 1881 <ref> Comoy, M. 1881. Etude pratique sur les marées fluviales. Gauthiers-Villars, Paris</ref>) display strong damping and delay in tidal propagation, especially for the low-waters. Tidal propagation over this complex shallow geometry resulted in a tidal bore that reached its largest amplitude at about 50 km from the mouth. The lower panels relate to the current situation. In the course of the 20th century, and especially in the period 1970-1980, the morphology of the estuary was greatly changed by artificial interventions. The estuarine main channel was deepened, especially in the mouth zone, and fixed by submerged dikes. Large parts of the intertidal areas were diked and filled with dredged materials. Tidal damping and tidal distortion were greatly reduced. At present a small tidal bore occurs only under extreme tides and further inland than in the past.]]<br />
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[[Image:ConvergingEstuarySchematization.jpg|right|450px|thumb|Figure 7. Schematization of a strongly converging estuary. (a) Plan view; (b) 3D view.]]<br />
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As discussed before, the expansion of the tidal flood wave over large intertidal areas decreases its height and propagation speed. The opposite occurs when the tide propagates into a tidal channel that becomes progressively narrower in up-channel direction, see Fig. 7. Instead of expanding laterally, the tidal wave is contracted when propagating. In the hypothetical case of no friction, conservation of the tidal energy flux along the channel requires up-channel amplification of the tidal amplitude (according to Green's law<ref name=J>Jay, D.A. 1991. Green's law revisited: tidal long-wave propagation in channels with strong topography. J.Geophys.Res. 96: 20,585-20,598</ref>). Many estuaries with significant river inflow have an upstream converging channel. Intertidal areas are rather small, partly as a result of natural sedimentation but often also as a result of human reclamation. The channel depth along the thalweg is fairly uniform<ref name=Sa>Savenije, H.H.G. 2012. Salinity and Tides in Alluvial Estuaries, second ed., Salinity and Tides in Alluvial Estuaries, second ed., www.salinityandtides.com </ref>, but shoals may be present in the mouth zone. The uniformity of the depth can also be due to dredging works for navigation purposes. <br />
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Insight in the role of the most important nonlinear terms can be gained when simplifications are made. In the following we consider an idealized estuary with exponentially converging width. The corresponding estuarine geometry is shown in Fig. 7. The mean water depth <math>h</math> is uniform throughout the estuary; the channel width <math>B</math> converges exponentially and the intertidal width <math>B_I</math> increases linearly from the LW level up to the HW level, <br />
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<math>B_C = b_c e^{-x/L_b} , \; B_I = e^{-x/L_b} \Delta b (1 + \zeta / h), \; <b> = b_C+\Delta b. \quad \quad (12)</math><br />
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It should be borne in mind that although many estuaries have an upstream converging width, the assumption of exponential width convergence and uniform depth is for most estuaries a very rough approximation. Often only a limited part of the estuary can be represented in this way. <br />
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Tidal propagation in this part of the estuary can be described by the mass and momentum balance equations (5) and (6). The instantaneous local depth is <math>D(x,t)=h+\zeta(x,t)</math> and the cross-sectional averaged tidal velocity is <math>u(x,t)</math>. Density gradients are left out of consideration. When substituting the expressions (12) for the width and omitting all nonlinear terms we obtain<br />
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<math> \Large \frac{<b>}{b_C} \frac{\partial \zeta}{\partial t}\normalsize + h \Large \frac{\partial u}{\partial x}\normalsize – u \Large \frac{h}{L_b} \normalsize = 0 . \quad \quad (13)</math><br />
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<math>\Large\frac{\partial u}{\partial t}\normalsize + g \Large \frac{\partial \zeta}{\partial x}\normalsize + r \Large \frac{u}{h}\normalsize = 0 . \quad \quad (14)</math><br />
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Solving these linear equations (only tide, no river discharge) yields <br />
<br />
<math>\zeta = a e^{-\mu x} \; cos(kx-\omega t) \quad </math> with <math>\quad 2 L_b \; \mu = \normalsize -1 + \Large[\normalsize 1 – (\Large \frac{1}{2} \normalsize + 2 K_0^2) +\large[\normalsize (\Large \frac{1}{2}\normalsize + 2 K_0^2 )^2+ 4 (K_c^2 - K_0^2) \large]^{\large 1/2} \Large]^{\large 1/2} \normalsize, \quad \quad (15)</math><br />
<br />
where <math>K_0 = \Large \frac{\omega L_b}{\sqrt{ghb_C/<b>}}\normalsize , \; K_c = \Large \frac{r \omega L_b^2<b>}{g h^2b_C} \normalsize </math>. The damping factor <math>\mu</math> is positive for large friction and large convergence length (<math>K_c >K_0</math>). However, for small friction and small convergence length (<math>K_c <K_0</math>) the damping factor is negative: the tide is amplified when propagating up-channel. Even in the case of strong friction, the tide is only slightly damped or even amplified if the convergence length <math>L_b</math> is sufficiently small. In cases where tidal damping dominates over the effect of channel convergence (large <math>L_b</math>), the relative tidal amplitude decreases along the estuary; tidal asymmetry then becomes less relevant for upstream sediment transport. As noted before, the friction factor <math>r</math> can vary greatly between estuaries because of salinity stratification and the type of bed sediments (coarse or muddy). <br />
<br />
The solution of the Eqs. (13) and (14) also yields an expression for the wave propagation velocity <math>c</math>:<br />
<br />
<math>c = \Large \frac{\omega}{k}\normalsize = 2 \omega L_b \Large[\normalsize - 1 + (\Large \frac{1}{2} \normalsize + 2 K_0^2) +\large[\normalsize (\Large \frac{1}{2}\normalsize + 2 K_0^2 )^2+ 4 [K_c^2 - K_0^2] \large]^{\large 1/2} \Large]^{\large -1/2}\normalsize . \quad \quad (16)</math><br />
<br />
<br />
The expressions (15) and (16) show that tidal wave propagation depends on only two parameters, <math> K_0</math> and <math> K_c </math>. The linear equations (13) and (14) do not describe tidal wave deformation; for this, nonlinear terms have to be included (<math>u \partial u /\partial x</math> and time varying water depth <math>h+\zeta</math> in Eq. (13) and <math>b \zeta \partial u / \partial x</math> in Eq. (14)). <br />
<br />
In strongly converging friction-dominated estuaries the nondimensional wave numbers <math> K_0</math> and <math> K_c </math> have similar order of magnitude (consider, for example, <math>r \approx</math> 0.003 m/s, and the typical geometries <math>\Delta b <<b_C</math>, convergence length <math>L_b \approx</math> 25 km and depth <math>h \approx</math> 8 m, or convergence length <math>L_b \approx</math> 10 km and depth <math>h \approx</math> 5 m). In this case <math>\mu \approx 0</math>: the longitudinal variation of the tidal amplitude is small. Although friction causes damping of the tidal amplitude along the estuary, observations show that the tidal amplitude in many estuaries is fairly uniform along the estuary (Friedrichs and Aubrey, 1994<ref name=Fr> Friedrichs C.T. and Aubrey, D.G. 1994. Tidal propagation in strongly convergent channels. J.Geophys.Res. 99: 3321-3336</ref>; Prandle, 2004<ref> Prandle, D. 2004. How tides and river flows determine estuarine bathymetries. Progress in Oceanography 61: 1–26</ref>; Savenije, 2012<ref name=Sa></ref> ); see also the article [[Physical processes and morphology of synchronous estuaries]]. The reason is that tidal amplification by the funneling effect approximately cancels tidal damping due to friction. In a strongly, exponentially converging estuary the tide is propagating upstream with a phase difference of approximately 90° between tidal elevation and tidal velocity (Jay, 1991<ref name=J></ref>). In some estuaries the funneling effect even produces an increase of the tidal amplitude in the strongly converging part of the estuary; examples are the [[Morphology of estuaries#Hooghly estuary|Hooghly]] (Fig. 1), [[Morphology of estuaries#Western Scheldt and Scheldt estuary|Scheldt]], Humber, Gironde-Garonne. <br />
<br />
In the case of strong friction and strong exponential width convergence, the tidal equations (5) and (6) can be simplified by neglecting the term <math>B_C \partial (Du) / \partial x</math> compared to <math>Du \partial B_C / \partial x</math> in Eq. (5) and the terms <math>\partial u / \partial t</math>, <math> u \partial u / \partial x</math> compared to <math>ru/h</math> in Eq. (6). The two simplified equations can be combined by eliminating <math>u</math>. This yields the simple characteristic equation<br />
<br />
<math>\Large\frac{d}{dt}\normalsize \zeta(x(t),t) = 0 , \quad \Large\frac{d x(t)}{dt}\normalsize = c = \Large\frac{g b_C D^2}{r b_S L_b}\normalsize . \quad \quad (17)</math><br />
<br />
If the relative tidal amplitude <math>a/h</math> and the relative intertidal area <math>\Delta b / b_C</math> are small, the HW propagation velocity <math>c^+</math>, and LW propagation velocity <math>c^-</math> follow directly from Eq. (17): <br />
<br />
<math> c^{\pm} \approx \Large\frac{g b_C h^2}{r L_b <b>}\normalsize \; (1 \pm \Large\frac{2a}{h}\normalsize \mp \Large\frac{\Delta b}{<b>}\normalsize ) . \quad \quad (18)</math><br />
<br />
A similar expression was already obtained by Friedrichs and Aubrey (1994) <ref name=Fr></ref> from an analytical model of converging estuaries with small relative tidal amplitudes and small intertidal areas. The role of the nonlinear terms for tidal distortion is similar as for the prismatic channel. The nonlinearity in the friction term Eq. (7) implies less friction in the period around HW compared to the period around LW and a corresponding increase of the HW propagation speed compared to the LW propagation, yielding positive tidal asymmetry. The nonlinearity related to the width increase with rising water level Eq. (8) implies a decrease of the HW propagation velocity compared to the LW propagation, yielding negative tidal asymmetry.<br />
<br />
[[Image:CharenteSpringNeapTide.jpg|left|350px|thumb|Figure 8: Tidal elevation (solid) and current velocity (dotted) curves in the Charente estuary for springtide (red) and neap tide (blue). The spring tidal curves exhibit a steep tidal rise and flood currents that are stronger than ebb currents. Hardly any tidal asymmetry occurs during neap tide and ebb currents are stronger than flood currents. Data from Toublanc et al. (2015) <ref>Toublanc, F., Brenon, I., Coulombier, T. and LeMoine, O. 2015. Fortnightly tidal asymmetry inversions and perspectives on sediment dynamics in a macrotidal estuary (Charente, France). Continental Shelf Res. 94: 42–54</ref>. Characteristic parameters for the Charente estuary are: channel depth <math>h \approx</math> 6.5 m, convergence length <math>L_b \approx</math> 10 km.]]<br />
<br />
The examples of tidal propagation in a prismatic channel and tidal propagation in a strongly converging estuary show that strong positive tidal asymmetry will develop only in estuaries with a large relative tidal amplitude <math>a/h</math> and small relative intertidal area <math>\Delta b / b_C</math>. The analytic models can only be evaluated for small values of <math>a/h</math>. However, the physical mechanisms for the development of strong tidal asymmetry are basically the same when <math>a/h</math> is no longer a small quantity, as confirmed by fully nonlinear mathematical models (Peregrine, 1966<ref> Peregrine, D.H. 1966. Calculations of the development of an undular bore J. Fluid Mech. 25: 321–30</ref>; Filippini, 2019<ref> Filippini, A.G., Arpaia, L., Bonneton, P. and Ricchiuto, M. 2019. Modeling analysis of tidal bore formation in convergent estuaries. European Journal of Mechanics - B/Fluids 73: 55-68</ref>). The importance of the parameter <math>a/h</math> for the development of positive tidal asymmetry is illustrated by observations that show a positive tidal asymmetry at spring tide and a negative tidal asymmetry at neap tide in the Pungue estuary (Mozambique; Nzualo et al., 2018<ref> Nzualo, T.N.M., Gallo, M.N. and Vinzon, S.B. 2018. Short-term tidal asymmetry inversion in a macrotidal estuary (Beira, Mozambique). Geomorphology 308: 107–117</ref>) and the [[Morphology of estuaries#Charente estuary|Charente estuary]] (France; Toublanc et al., 2015<ref> Toublanc, F., Brenon, I., Coulombier, T. and LeMoine, O. 2015. Fortnightly tidal asymmetry inversions and perspectives on sediment dynamics in a macrotidal estuary (Charente,France). Continental Shelf Res. 94: 42–54</ref>). This is illustrated in Fig. 8 for the [[Morphology of estuaries#Charente estuary|Charente estuary]], by comparing the curves for tidal elevation and current velocity for springtide (large <math>a/h</math>) and neap tide (small <math>a/h</math>). During springtide the tidal rise is much steeper than for neap tide. The maximum flood current velocity is larger than the maximum ebb tidal velocity for springtide, while the opposite holds for neap tide. <br />
<br />
[[Image:TidalAsymmetryEstuaries.jpg|right|350px|thumb|Figure 9: The relative tidal amplitude <math>a/h</math> and corresponding relative difference between HW and LW propagation speed <math>\Delta c / c</math> for different estuaries, derived from tide gauge stations in the converging part of the estuary. Adapted from<ref name=Dr></ref>.]]<br />
<br />
In Fig. 9 the relative difference between HW and LW propagation speeds <math>\Delta c / c = 2(c^+ -c^-)/(c^++c^-)</math> are compared for estuaries with different relative tidal amplitude <math>a/h</math>. The figure shows a positive correlation between <math>\Delta c / c </math> and <math>a/h</math>. Although <math>a/h</math> is the most important parameter, other factors also influence the relation between <math>a/h</math> and <math>\Delta c / c</math>, such as <math>K_0</math> and <math>K_c</math> (representing depth <math>h</math>, convergence length <math>L_b</math> and friction parameter <math>r</math>), the relative intertidal area <math>\Delta b/b_C</math> and the mean river discharge <math>Q_R</math>. The dependence of <math>\Delta c / c </math> on <math>a/h</math> is therefore different for each estuary. <br />
<br />
Equation (18) yields an estimate for the location <math>x</math> where the high-water wave crest overtakes the low-water wave trough, assuming that the tide at the estuarine mouth (<math>x=0</math>) is approximately symmetric and assuming that Eq. (18) remains approximately valid in the strong nonlinear case. For an estuary with small intertidal areas the distance <math>x</math> is given by<br />
<br />
<math>x = \Large\frac{\pi}{4}\frac{gh^2}{\omega r L_b}\frac{h}{a}\normalsize . \quad \quad (19)</math><br />
<br />
For example, in the case of the Gironde-Garonne estuary and tidal river system (<math>a \approx 2.5 m, h \approx 8 m, L_b \approx 35 km, r \approx 0.0025 m/s</math>) we find <math>x \approx 130 </math> km from the estuarine mouth, which is close to the location where a tidal bore is often observed. This example shows that a tidal bore will form if (1) frictional damping of the tidal wave is compensated by the funneling effect of width convergence and (2) the distance over which the tide can propagate into the estuary is sufficiently long (see also the article [[Tidal bore dynamics]]). <br />
<br />
In estuaries where frictional damping is not compensated by the funneling effect of width convergence, tidal asymmetry is generated in a similar way by the nonlinear processes described above (Friedrichs and Madsen, 1992<ref> Friedrichs, C.T. and Madsen, O.S. 1992. Non-linear diffusion of the tidal signal in frictionally dominated embayments. J.Geophys.Res. 97: 5637-5650</ref>). However, reduction of the relative tidal amplitude <math>a/h</math> by damping of the tidal wave may prevent tidal bore development. <br />
<br />
<br />
==Morphology of estuaries with tidal rivers==<br />
<br />
In a converging (funnel-shaped) estuary with strong friction, the tidal velocity <math>u</math> is mainly determined by the water surface slope <math>\partial \zeta /\partial x</math>, according to Eq. 14. A short period of tidal rise compared to the period of tidal fall implies steeper water surface slopes during flood than during ebb, with maximum flow rates that are higher during flood than during ebb, as illustrated in Fig. 8. Therefore, sediment fluxes during flood tide are higher than sediment fluxes during ebb tide, resulting in a net import of sediment into the estuary. As shown before, flood dominance increases with increasing relative tidal amplitude <math>a/h</math>. The time span over which flood dominance develops also plays a role. For converging estuaries the relevant nondimensional time duration indicator is mainly determined by the ratio of convergence length and tide propagation speed <math>L_b \omega/ c</math>. The value of the nondimensional parameter <math>a L_b \omega / (h c)</math> can be considered an indication for the strength of flood dominance. <br />
<br />
[[Image:TidalAsymmetryRiverFlow.jpg|right|400px|thumb|Figure 10: Tidal asymmetry indicator versus river flow indicator for different estuaries. A positive correlation is an indication that river flow makes an important contribution to compensating for tide-induced sediment import. The spread in the data is related to many other factors that influence sediment import/export. Adapted from <ref name=D17>Dronkers, J. 2017. Convergence of estuarine channels. Continental Shelf Res. 144: 120–133</ref>.]]<br />
<br />
Infill of estuaries is limited by sediment export through river flow, although dredging may also play a role. The influence of river flow on sediment export can be represented by the nondimensional parameter <math>Q_R/Q_{tide}</math>, where <math>Q_R</math> is the mean river discharge and <math>Q_{tide}</math> the maximum tidal discharge in the mid-estuarine zone (<math>x \approx L_b/2</math>). For estuaries in morphological equilibrium, sediment import due to tidal asymmetry (flood dominance) should be approximately balanced by export due to river flow. Comparing different estuaries one may thus expect a positive correlation between the parameters <math>a L_b \omega / (h c)</math> and <math>Q_R/Q_{tide}</math> <ref name=D17></ref>. As shown in Fig. 10, such a positive correlation exists, although the spread in the data is large. This spread can be due to many other factors, which influence sediment import and export in different ways. Possible important factors are<ref name=Dr></ref>:<br />
* dredging,<br />
* import/export by [[Morphology of estuaries#Wave-dominated systems|wave activity]],<br />
* import by [[estuarine circulation]],<br />
* sediment recirculation in ebb/flood-channel cells,<br />
* sediment import/export related to settling and erosion time lags,<br />
* fluvial sediment supply,<br />
* type of [[Coastal and marine sediments|sediment]].<br />
<br />
<br />
==Related articles==<br />
:[[Morphology of estuaries]]<br />
:[[Ocean and shelf tides]]<br />
:[[Tidal bore dynamics]]<br />
:[[Tidal motion in shelf seas]]<br />
:[[Estuarine circulation]]<br />
<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
==Appendix==<br />
<br />
The solution of the first order linear equations (1) and (2) is <br />
<br />
<math>\zeta^{(1)}=a \cos \theta , \; u^{(1)} = \Large\frac{c_0}{h}\normalsize \zeta^{(1)} , \quad \quad (A1)</math> <br />
<br />
where <math>\theta= k_0 x-\omega t</math>, <math>\omega</math> is the M2 radial frequency, the wave number <math>k_0 = \Large \frac{\omega}{gh} \normalsize</math> and <math>c_0=\omega / k</math>. <br />
<br />
After substitution in the nonlinear terms we have a linear equation for the second order approximation. The solution is<br />
<br />
<math>\zeta = \zeta^{(1)} + \zeta^{(2)} , \quad \zeta^{(2)} = \Large \frac{3 a^2}{4h}\normalsize kx \sin 2 \theta . \quad \quad (A2)</math><br />
<br />
The location of the wave crest at time <math>t</math> is called <math>x^+(t) </math>. At this location the surface slope is zero:<br />
<br />
<math> \Large \frac{\partial \zeta}{\partial x}\normalsize (x^+(t),t) = -a k_0 \sin \theta^+ + \Large \frac{3 a^2}{4h}\normalsize k_0 [ \sin 2 \theta^+ + 2kx \cos 2 \theta^+ ] = 0 \quad </math> , with <math>\theta^+=k_0 x^+(t) - \omega t . \quad \quad (A3)</math><br />
<br />
Because <math>a/h</math> is small, the wave crest is at a location where <math>\theta^+</math> is small (<math>|\theta^+ |<<1</math>). An approximate expression for the location of the wave crest is then given by <br />
<br />
<math>x^+(t) \approx (1 - \Large \frac{3a}{2h}\normalsize)^{-1} c_0 t . \quad \quad (A4)</math>. <br />
<br />
The propagation speed of the HW wave crest (Eq. A4) follows from <math>c^+(t)=dx^+/dt</math>. <br />
<br />
The first order linear equations (9) and (10) can be solved by eliminating <math>u(x,t)</math>, yielding a diffusion equation for the tidal elevation <math>\zeta(x,t)</math>:<br />
<br />
<math>\Large\frac{\partial \zeta^{(1)} }{\partial t}\normalsize = \Large\frac{h^2}{r}\frac{B_C}{<B>}\frac{\partial^2 \zeta^{(1)} }{\partial x^2}\normalsize .\quad \quad (A5)</math><br />
<br />
The first order solution is<br />
<br />
<math>\zeta^{(1)} = \Large\frac{1}{2}\normalsize a e^{i (\kappa x - \omega t)} + c.c. </math>, <br />
where <math>c.c. </math> is the complex conjugate, <math>\kappa = k+i \mu , \; k = \mu = \sqrt { \Large \frac{\omega r}{2 g h^2}\normalsize }. \quad \quad (A6) </math><br />
<br />
After substitution in the nonlinear terms the second order linear equations can be solved, yielding<br />
<br />
<math>\zeta = \zeta^{(1)} + \zeta^{(2)} , \quad \zeta^{(2)} \approx a (\Large \frac{\Delta b}{8 B_C} - \frac{a}{2h}\normalsize) e^{-2i \omega t} (e^{2i \kappa x} -e^{\sqrt{2} i \kappa x} ) + \Large \frac{a^2}{4h}\normalsize (1 – e^{-2 \mu x}) + c.c. \quad \quad (A7)</math><br />
<br />
In the same way as before the location of the wave crest is derived from the condition <br />
<br />
<math> \Large \frac{\partial \zeta}{\partial x} \normalsize (x^+(t),t) =0</math> for <math>| k x^+ - \omega t|<< 1</math>. <br />
<br />
The propagation speed of the HW wave crest (Eq. 11) follows from <math>c^+(t)=dx^+/dt</math>; this expression holds for the lower portion of the estuary where <math>kx<<1</math>.<br />
<br />
<br />
<br />
<br />
{{2Authors<br />
|AuthorID1=120<br />
|AuthorFullName1=Job Dronkers<br />
|AuthorName1=Dronkers J<br />
|AuthorID2=15152<br />
|AuthorFullName2= Philippe Bonneton <br />
|AuthorName2= Bonneton P<br />
}}<br />
<br />
<br />
[[Category: Physical coastal and marine processes]]<br />
[[Category: Estuaries and tidal rivers]]<br />
[[Category: Morphodynamics]]<br />
[[Category:Hydrodynamics]]</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Tidal_asymmetry_and_tidal_basin_morphodynamics&diff=76283Tidal asymmetry and tidal basin morphodynamics2019-12-16T16:55:26Z<p>Dronkers J: </p>
<hr />
<div><br />
This article describes the physical processes responsible for tidal wave deformation in shallow coastal inlet systems – tidal lagoons and estuaries. A qualitative discussion is given of the mutual interaction between tidal asymmetry generation and morphological development of these systems, which is generally referred to by the term ''self-organizing morphodynamics''. This article is largely based on the book ''Dynamics of Coastal Systems'' <ref name=Dr>Dronkers, J. 2017. Dynamics of Coastal Systems. World Scientific Publ. Co, Singapore, 740 pp.</ref>. <br />
<br />
==Tidal wave deformation in shallow water==<br />
<br />
Tides result from the response of the ocean water bodies to the attractive gravitational forces by sun and moon. Tidal motion in the oceans can be described by a limited number of sinusoidal components, because earth's rotation and the relative movements of earth, sun and moon have a cyclical character, see the article [[Ocean and shelf tides]]. The semidiurnal lunar tide (M2) is usually the dominant component, in which case the ocean tide can be described fairly accurately with a single sine function.<br />
<br />
Ocean tidal waves are distorted when they propagate into shallow coastal waters. Here the term tidal wave distortion is to be understood as a systematic (long-term averaged) difference between the periods of rising and falling tide, also called tidal asymmetry. We will use the term positive duration asymmetry for tides with a longer fall and shorter rise and negative duration asymmetry for tides with a shorter fall and longer rise. Nonlinear hydrodynamic processes that are insignificant in the deep ocean become important when the tidal range is larger than a small fraction of the mean water depth. In the following we shortly review the major nonlinear processes involved in initiating shallow-water tidal distortion. <br />
<br />
However, it must be noted before that linear ocean tides are not fully symmetric, due to the superposition of certain tidal components with mutually related frequencies (for example, the sum of the frequencies of the K1 and O1 tides is equal to the frequency of the M2 tide). Although this was known for a long time (Doodson, 1921)<ref> Doodson, A.T. 1921. The harmonic development of the tide-generating potential. Proc.R.Soc.London, Ser.A 100: 305-329</ref>, it has received renewed attention more recently due to the observations and analyses of Hoitink et al. (2003)<ref> Hoitink, A.F.J., Hoekstra, P. and van Mare, D.S. 2003. Flow asymmetry associated with astronomical tides: Implications for residual transport of sediment. J.Geophys.Res. 108: 13-1 - 13-8</ref> and several other studies since (Nidzieko, 2010<ref>Nidzieko, J. 2010. Tidal asymmetry in estuaries with mixed semidiurnal/diurnal tides. J. Geophysical Research 115, C08006, doi:10.1029/2009JC005864</ref>; Zhang, 2018 <ref>Zhang, W., Cao, Y., Zhu, Y., Zheng, J., Ji, X., Xu, Y., Wu, Y. and Hoitink, A.F.J. 2018. Unravelling the causes of tidal asymmetry in deltas. Journal of Hydrology 564: 588–604</ref>). A world map showing ocean regions with [[Ocean and shelf tides#Asymmetric ocean tides|asymmetric tides]] was published by Song et al. (2011<ref> Song, D., X. H. Wang, A. E. Kiss, and Bao, X. 2011. The contribution to tidal asymmetry by different combinations of tidal constituents. J. Geophys. Res., 116, C12007</ref>), based on tidal constants derived from the TPXO7-ATLAS (http://volkov.oce.orst.edu/tides/atlas.html). Asymmetric tides (with either positive or negative duration asymmetry) occur mainly in regions where tides have a mixed character, with comparable magnitudes of diurnal and semidiurnal tidal components. <br />
<br />
Although the asymmetry of ocean tides can be significant, tidal asymmetry can become much stronger due to the generation of shallow-water overtides in shallow coastal areas with a large semidiurnal tidal range (dominated by M2). The distortion of the tide can be so strong that the durations of rising tide and falling tide become very different and that a large difference arises between the peak flow velocities of flood and ebb. Often the duration of rising tide is much shorter than the duration of falling tide. This is illustrated in Fig. 1 for the [[Morphology of estuaries#Hooghly estuary|Hooghly estuary]]. In the most extreme case, the duration of tidal rise becomes so short that a hydraulic jump develops at the front of the tidal wave. The front of the tidal wave appears as a propagating wall of water, a so-called tidal bore, as explained in the article [[Tidal bore dynamics]]. <br />
<br />
<br />
[[Image:HooghlyTidalWaveDeformation.jpg|center|700px|thumb|Figure 1: Tide curves in the Hooghly estuary observed during a high springtide (19/9/2009) at different tide gauges along the estuary. Data from Banerjee et al. (2015)<ref>Banerjee, A.P., Dutta, S. and Majumdar, A. 2015. Quest for the determination of environmental flow assessment for hilsa fish of the Hooghly estuary by hydraulic rating method. ARPN Journal of Engineering and Applied Sciences 10: 7885-7899</ref>]]<br />
<br />
<br />
We focus here on asymmetry generated by the interaction of tides with topographic characteristics. Most studies of overtide generation consider estuaries and tidal rivers with simple one-dimensional geometries. In these studies, the influence of channel curvature, secondary channels or local channel constrictions on tidal asymmetry are ignored. Asymmetries related to density gradients or wind-driven currents are also left out of consideration. <br />
<br />
<br />
==Tidal wave deformation in the absence of friction==<br />
<br />
The distortion of the tide described above is related to a difference in propagation speed of the high-water crest of the tidal wave and the low-water trough. This difference already occurs when the water depth below the wave crest is slightly greater than the water depth below the wave trough. This can be easily demonstrated for a tidal wave that propagates in <math>x</math>-direction with time <math>t</math> in deep water with little loss of friction. The most simple geometry is an infinite prismatic channel. The mean (tide-averaged) channel depth is called <math>h</math> (constant), the tidal elevation is called <math>\zeta(x,t)</math>, the total instantaneous water depth <math>D(x,t)=h+\zeta(x,t)</math> and the cross-sectionally averaged velocity <math>u(x,t)</math>. <br />
<br />
In the absence of friction, the tidal equations for mass and momentum read:<br />
<br />
<math>\Large\frac{\partial \zeta}{\partial t}\normalsize +\Large\frac{\partial(Du)}{\partial x}\normalsize=0 , \quad \quad (1)</math><br />
<br />
<math>\Large\frac{\partial u}{\partial t}\normalsize + u \Large\frac{\partial u}{\partial x} \normalsize + g \Large\frac{\partial \zeta}{\partial x}\normalsize = 0 , \quad \quad (2)</math><br />
<br />
where <math>g</math> is the gravitational acceleration. Overtides are due to the nonlinear terms <math>\partial(\zeta u) / \partial x </math> and <math> u \partial u / \partial x</math>. The quadratic nature of these terms implies that the first and most important overtide (M4) has twice the frequency of the M2 tide. The tidal equations (1,2) can be cast in the form of a characteristic equation that describes the propagation of the tidal wave <math>\zeta(x,t)</math> in positive x-direction,<br />
<br />
<math>\Large\frac{d}{dt}\normalsize \zeta(x,t) = 0 , \quad \Large\frac{dx}{dt}\normalsize = 3 c + u_0 – 2 c_0 , \quad \quad (3)</math><br />
<br />
where <math>c=\sqrt{gD(x,t)} , \; c_0= \sqrt{gD(0,0)} , \; u_0=u(0,0) .</math> A derivation is given in appendix A. We choose <math>x=0, t=0</math> at high water (HW) and assume that the relative tidal amplitude <math>a/h</math> during the time <math>t</math> remains small (<math> a/h << 1</math>). Then we have <math>D(0,0) \approx h+a , \; u(0,0) \approx a\sqrt{g/h}</math> as first-order solution of Eqs. (1) and (2). According to Eq. (3), HW thus propagates with velocity<br />
<br />
<math>c^+ = 3 c + u_0 – 2 c_0 = 3 \sqrt{g(h+a)} + a \sqrt{g/h} – 2 \sqrt{g(h+a)} \approx \sqrt{gh} (1 + \Large\frac{3a}{2h}\normalsize) . \quad \quad (4)</math><br />
<br />
<br />
[[Image:PropagatingWaveDeformation.jpg|right|400px|thumb|Figure 2: Deformation of a frictionless propagating wave. The blue curve is the sinusoidal tidal wave with amplitude <math>a</math> of 2 m, at <math>\small x=0</math>, <math>\small\zeta(x=0,t) = a \cos \omega t</math>. The red curve is the distorted tidal wave after travelling a distance of <math>\small x=</math> 100 km without friction in a channel of 10 m mean depth, according to the second-order solution of Eqs. (1) and (2) for <math>a/h<<1</math>, which is given by <math>\small \zeta(x,t) = \zeta^{(1)} + \zeta^{(2)} </math>, with <math>\small \zeta^{(1)} = a \cos(\omega t - kx)</math>, <math>\small\zeta^{(2)} = \large\frac{3 a^2}{4h} \small kx \sin(2 \omega t – 2kx) </math> (see appendix B). The dotted red line is the M4 overtide <math>\small \zeta^{(2)} </math>. The red curve displays a shorter tidal rise and a longer tidal fall: the tidal wave crest has propagated faster than the tidal wave trough.]]<br />
<br />
In the same way one finds for the propagation velocity of the low-water (LW) location <math>c^- \approx \sqrt{gh} (1 – \frac{3a}{2h})</math>. Another method to find this result is presented in appendix B. As HW propagates faster than LW, the tidal wave front will steepen progressively; the duration of rising tide shortens while the duration of falling tide is lengthened. This positive tidal asymmetry increases with the relative tidal amplitude <math>a/h</math> as a consequence of the nonlinear terms <math>\partial(\zeta u) / \partial x </math> and <math> u \partial u / \partial x</math> in the tidal equations. The resulting tidal distortion is illustrated in Fig. 2. Equation (4) suggests that after some time the high-water wave crest will overtake the low-water wave trough. However, this can only happen when the amplitude of the M4 overtide is of the same order of magnitude as the M2 tide, which violates the approximations used in Eq. (4).<br />
<br />
The tidal equations for a prismatic channel do not well represent tidal propagation in estuaries because of neglect of the friction term. The equations (1,2) are more representative for the [[Coriolis and tidal motion in shelf seas|along-shore propagation of a tidal Kelvin wave]], far away from hard boundaries where the tidal wave can reflect or from hydrodynamic boundaries where the Kelvin wave meets other tidal wave systems. An increasing tidal asymmetry develops in situations where the coastal zone is shallow and the tidal amplitude is large. The increasing tidal asymmetry along the coast of Normandy (France) can be understood in this way (Fig. 3), as well as the increasing tidal asymmetry along the North Sea coast of Holland (see: [[Coriolis and tidal motion in shelf seas]]). The tidal wave that enters estuaries situated along such coasts (the Seine at Le Havre, for instance) exhibits already significant positive-duration tidal asymmetry.<br />
<br />
<br />
[[Image:ChannelFrance.png|center|600px|thumb|Figure 3. Increasing positive asymmetry (<math>\Delta_{FR}</math> is the difference of the durations of tidal fall and tidal rise) of the tidal wave propagating along the coast of Normandy (France). Tide gauge data of 29 September 2015.]]<br />
<br />
<br />
==Tidal wave deformation in the presence of friction and intertidal areas==<br />
<br />
Tidal asymmetry develops during up-channel propagation into a shallow tidal basin. Pronounced tidal asymmetry (possibly leading to tidal bore formation) only occurs if during propagation a sufficiently large ratio <math>a/h</math> is maintained. In many cases this condition is not met, because the tidal amplitude decreases during propagation. The two main reasons for decrease of the tidal amplitude are: (1) tidal wave damping by friction and (2) lateral spreading of the flood tidal wave. These two nonlinear processes also influence the propagation of the high-water wave crest and the low-water wave trough. <br />
<br />
We consider a tidal basin where the longitudinal tidal flow <math>u(x,t)</math> is confined in a single tidal channel with depth <math>D(x,t)</math> and width <math>B_C(x)</math>. Flood water can spread over intertidal areas; the width of the intertidal area <math>B_I(x,t)</math> is a function of the water level <math>\zeta(x,t)</math>. The tidal propagation in this basin can be described by the mass and momentum balance equations<br />
<br />
<math>B \Large\frac{\partial \zeta}{\partial t}+\frac{\partial}{\partial x}\normalsize (B_C Du) = 0 , \quad \quad (5)</math><br />
<br />
<math>\Large\frac{\partial u}{\partial t}\normalsize + u \Large\frac{\partial u}{\partial x} \normalsize + g \Large\frac{\partial \zeta}{\partial x}\normalsize + F = 0 , \quad \quad (6)</math><br />
<br />
where <math>B= B_C+B_I </math> is the total surface width. The symbol <math>F</math> in Eq. (6) stands for the frictional momentum dissipation which is usually represented by a quadratic expression of the form <math>F= c_D \large\frac{|u|u}{D} </math>. Although it appears from detailed measurements that this expression is a rough approximation – the friction coefficient <math>c_D</math> is found to be variable both temporally and spatially (Lewis and Lewis, 1987<ref> Lewis, R. E., and Lewis, J. O. 1987. Shear-stress variations in an estuary. Estuarine Coastal Shelf Sci. 25: 621–635</ref>; Stacey and Ralston, 2005<ref name=SR> Stacey, M.T. and Ralston, D.K. 2005. The Scaling and Structure of the Estuarine Bottom Boundary Layer. J. Physical Oceanography 35: 55-71</ref>; Lefebvre et al., 2012<ref> Lefebvre, A., Ernstsen, V.B and Winter, C. 2012. Estimation of roughness lengths and flow separation over compound bedforms in a natural-tidal inlet. Continental Shelf Research 61–62: 98-111 </ref>) – we consider here a further approximation assuming that the quadratic dependence on <math>u</math> can be ignored: <math>F = r \large\frac{u}{D}</math>. Here, is <math>r</math> a constant friction coefficient with dimension [m/s] that relates momentum dissipation at the channel bed to the depth-averaged current velocity. Its value typically ranges between 0.001 - 0.004 m/s <ref name=Dr></ref>. The precise value of the friction coefficient for estuarine flow is generally not well known as it is influenced by many factors such as density stratification (lower friction), small bed forms (higher friction) and fluid mud layers (lower friction). The friction coefficient may even be different for ebb and flood because of differences in salinity stratification<ref name=SR></ref>. In most estuaries, the tidal discharge amplitude is much larger than the river discharge, which therefore does not strongly influence frictional dissipation in the absence of salinity stratification. In this case, the linearization of the friction term is a minor approximation compared to the uncertainty in the value of the friction coefficient.<br />
<br />
[[Image:PrismaticTidalFlatChannelNEW.jpg|right|300px|thumb|Figure 4: Prismatic estuarine channel with tidal flats.]]<br />
<br />
The tidal equations (5) and (6) are too complex for an analytic treatment in which tidal asymmetry is explicitly related to the nonlinear terms. An analytical solution of the tidal equations requires further approximations, by assuming that the contribution of nonlinear terms is relatively small and can be linearized (Lanzoni and Seminara, 1998<ref> Lanzoni, S. and Seminara, G. 1998. On tide propagation in convergent estuaries, J. Geophys. Res. 103: 30793–30812</ref>).<br />
<br />
Therefore we consider a prismatic tidal channel with a uniform mean depth <math>h</math> much larger than the tidal amplitude <math>a</math>, such that the friction term can be approximated by<br />
<br />
<math>F = r \Large\frac{u}{D}\normalsize =r \Large\frac{u(x,t)}{h+\zeta(x,t)}\normalsize \approx r\Large\frac{u(x,t)}{h}\normalsize (1 - \Large\frac{\zeta(x,t)}{h}\normalsize) . \quad \quad (7)</math> <br />
<br />
We further assume that the intertidal storage width <math>B_I</math> is much smaller than the channel width <math>B_C</math> and that it increases linearly with the water level <math>\zeta(x,t)</math> (see Fig. 4):<br />
<br />
<math>B_I = \Delta b (1 + \Large\frac{\zeta(x,t)}{h}\normalsize), \quad <B>=B_C+\Delta b . \quad \quad (8)</math> <br />
<br />
In shallow estuaries (<math>h \le 5 m</math>) with strong tides, the nondimensional friction coefficient <math>r / (h \omega)</math> is substantially larger than 1 (the symbol <math>\omega</math> is the M2 tidal frequency). In this case the inertial terms <math>\partial u / \partial x </math> and <math> u \partial u / \partial x</math> are much smaller than the friction term <math>F</math>.<br />
<br />
In prismatic well-mixed estuaries, where salinity stratification can be ignored and where frictional effects are much stronger than inertial effects, the one-dimensional cross-section-averaged tidal equations (5) and (6) for small values of <math>a/h</math> can be simplified to <br />
<br />
<math><B> \Large \frac{\partial \zeta}{\partial t} \normalsize + h B_C \Large \frac{\partial u}{\partial x}\normalsize + \Delta b \Large \frac{\zeta}{a} \frac{\partial \zeta}{\partial t} \normalsize + B_C \Large \frac{\partial (\zeta u)}{\partial x}\normalsize =0 , \quad \quad (9)</math><br />
<br />
<math>g\Large \frac{\partial \zeta}{\partial x}\normalsize + r \Large \frac{u}{h}\normalsize – r \Large \frac{u \zeta}{h^2}\normalsize =0 . \quad \quad (10)</math><br />
<br />
<br />
In such friction-dominated estuaries the tide does not travel as a propagating wave, but rather advances into the estuary through a diffusion-type process, as shown by Eq. (B5) and described by Blondeaux (1978) for the Saint Lawrence Estuary <ref name=LB> LeBlond, P. 1978. On tidal propagation in shallow rivers, J. Geophys. Res., 83: 4717–4721</ref>. The tidal wave crest does not coincide with the time of high water, but lags behind. The same applies to low water.<br />
<br />
The nonlinear terms in the tidal equations are much smaller than the linear terms if <math>\Delta b << B_C</math> and <math>a/h << 1</math>. In this case a first order solution <math>\zeta^{(1)}</math> can be found by substituting the solution of the linear equations in the nonlinear terms. The nonlinear terms then generate a small M4 tidal component <math>\zeta^{(2)}</math>, which affects the duration of tidal rise and tidal fall. This is because the propagation speed <math>c^+</math> of the high-water wave crest differs from the propagation speed <math>c^-</math> of the low-water wave trough (see appendix B):<br />
<br />
<math>c^{\pm} \approx [1 \pm (2 - \sqrt{2}) \Large\frac{a}{h}\normalsize \mp \Large\frac{\Delta b}{2B_C}\normalsize ] \; \sqrt{gh} \; \sqrt{ \Large\frac{2 \omega h}{r} \frac{B_C}{<B>}\normalsize} . \quad \quad (11) </math> <br />
<br />
where <math>\omega</math> is the M2 radial frequency. <br />
<br />
This expression exhibits the effect of other nonlinearities in tidal propagation than those considered in the example of the prismatic channel: the effect of intertidal areas in Eq. (9) and the effect of depth dependence of the friction term in Eq. (10). The nonlinearity in the friction term Eq. (7) implies less friction in the period around HW compared to the period around LW and a corresponding increase of the HW propagation speed compared to the LW propagation, yielding positive tidal asymmetry. The nonlinearity related to the width increase with rising water level represented by the third term in Eq. (9) implies a decrease of the HW propagation velocity compared to the LW propagation, yielding negative tidal asymmetry (Speer and Aubrey, 1985<ref> Speer, P.E. and Aubrey, D.G. 1985. A study of non-linear tidal propagation in shallow inlet/estuarine systems. Part II: theory. Estuarine, Coastal Shelf Sci. 21: 207-224</ref>). This is because the HW crest of the tidal wave is delayed when propagating into the estuary by diversion of flood water over the intertidal area, while the LW wave trough remains confined within the narrower channel when propagating into the estuary. Hence, shallowness of the channel (large <math>a/h</math>) and large intertidal area (large <math>\Delta b/B_C</math>) have counteracting effects on tidal wave distortion.<br />
<br />
==Morphology of shallow tidal basins with small river inflow==<br />
<br />
In the foregoing it was shown that the tidal wave that enters a shallow prismatic channel is distorted due to the opposite effects of friction and intertidal areas on the up-channel propagation of HW on the one hand and LW on the other. In short tidal basins, these effects are partially offset by the reflected tidal wave at the landward basin boundary<ref name=Dr></ref>. However, in the case of strong friction, the reflected tidal wave is much smaller than the incoming tidal wave in a large part of the basin. In this part of the tidal basin the tidal velocity <math>u</math> is mainly determined by the water surface slope <math>\partial \zeta /\partial x</math>, according to Eq. 10. A short period of tidal rise compared to the period of tidal fall implies steeper water surface slopes during flood than during ebb. Hence, maximum flood velocities are higher than maximum ebb velocities in the absence of significant river inflow. <br />
<br />
[[Image:EquilibriumTidalLagoonsNEW.jpg|right|500px|thumb|Figure 5: The relative tidal amplitude <math>a/h</math> versus the relative intertidal area <math>\Delta b/<B></math> for a large number of tidal basins with small (or without) river inflow. Many of these basins (but not all) are back-barrier tidal basins or tidal lagoons: basins that are semi-closed by a sand barrier at the entrance. The figure shows a positive correlation between <math>a/h</math> and <math>\Delta b/<B></math>. The correlation between these basin characteristics also depends on other parameters, in particular the tidal asymmetry already existing at the basin entrance, which is different for each basin. Therefore, one should not expect that all the point lie on a single line. Adapted from<ref name=Dr></ref>.]]<br />
<br />
Because the transported sediment load increases more than linearly with the current velocity (see the articles [[Sand transport]] and [[Sediment transport formulas for the coastal environment]]), sediment fluxes during flood tide are higher than sediment fluxes during ebb tide. Flood-dominant tidal asymmetry thus produces a net import of sediment into the basin. Sediment infill could possibly go on until no tidal basin is left. This has happened in the past to some tidal basins, but many tidal basins without river inflow still survive. The reason is that flood dominance is neutralized by several processes. One of these processes is wave action, which can suspend large amounts of sediment in the HW period that are subsequently transported out of the basin by ebb currents<ref>Friedrichs, C.T. 2011. Tidal Flat Morphodynamics: A Synthesis. In: Treatise on Estuarine and Coastal Science, vol. 3, Estuarine and Coastal Geology and Geomorphology. Ed.:J. D. Hansom and B. W. Fleming, Elsevier, Amsterdam: 137-170</ref><ref> Desguée, R., Robin, N., Gluard, L., Monfort, O., Anthony, E.J., Levoy, F. 2011. Contribution of hydrodynamic conditions during shallow water stages to the sediment balance on a tidal flat: Mont-Saint-Michel bay, Normandy, France. Estuarine<br />
Coastal Shelf Sci. 94: 343–354</ref>. However, tidal basins do not depend only on wave action for their survival. One reason is the so-called Stokes transport, the water outflow compensating for the net influx due to greater mean water depth during flood than during ebb. Another reason is the reduction of tidal asymmetry due to the presence of intertidal areas as discussed in the previous section. During the development of intertidal areas by flood-dominant sediment transport, tidal asymmetry is weakened until the average sediment transport by flood currents has become comparable to the average transport by ebb currents. In order to neutralize flood dominance with increasing relative tidal amplitude <math>a/h</math>, the counteracting effect of intertidal areas should also increase. Fig. 5 shows that this is indeed the case for natural tidal basins with small (or without) river inflow: tidal basins with larger relative tidal amplitude have larger intertidal areas. One may thus conclude that self-organizing processes can produce a natural equilibrium morphology for tidal basins in a sedimentary environment without geological constraints<ref name=Dr></ref> <ref>Dronkers, J. 1998. Morphodynamics of the Dutch Delta. In: Physics of estuaries and coastal seas. Ed.: J.Dronkers and M.B.A.M. Scheffers, Balkema, Rotterdam: 297-304</ref> (see also the article [[Morphology of estuaries]]). <br />
<br />
<br />
==Tidal wave deformation in a converging channel==<br />
<br />
The influence of friction on tidal propagation increases with decreasing depth. The LW propagation is slowed down more strongly than the HW propagation, which results in a larger tidal asymmetry. However, the tidal amplitude is decreased by frictional damping. During the past century many estuaries have been deepened for navigational purposes and intertidal areas have been reclaimed. The effect of these interventions on tidal propagation is illustrated in Fig. 6 for the Seine estuary and tidal river system. The tide propagates now much faster into the estuary and the tidal amplitude is much larger, especially in the upstream river. The tide propagation speed has increased more for the low waters than for the high waters, although the propagation of the high waters also benefits of the reduction of the intertidal areas. In the past a high tidal bore developed each spring tide in the downstream river. After the interventions (especially the dredging of the mouth bar) it takes a much larger distance before the HW wave crest overtakes the LW wave trough. A small tidal bore now develops far upstream and only for very high tidal coefficients<ref> Bonneton, N., Bonneton, P., Parisot, J-P., Sottolichio, A. and Detandt G. 2012. Tidal bore and Mascaret - example of Garonne and Seine Rivers. Comptes Rendus Geosciences, 344, 508-515</ref>. <br />
<br />
<br />
[[Image: SeineTidalDeformation.jpg|center|800px|thumb|Figure 6: Tidal wave distortion in the Seine estuary. The figures at the left show simultaneously recorded tide curves during springtide, for locations at various distances from the estuarine mouth. The images on the right show the morphology of the Seine estuary. The upper figures relate to the situation in the 19th century, when the morphology of the Seine estuary was almost in a natural state, with large shoals at the mouth (mouth bars) and an inner system with multiple channels and extensive intertidal areas. The 1876 tide curves (Comoy, 1881 <ref> Comoy, M. 1881. Etude pratique sur les marées fluviales. Gauthiers-Villars, Paris</ref>) display strong damping and delay in tidal propagation, especially for the low-waters. Tidal propagation over this complex shallow geometry resulted in a tidal bore that reached its largest amplitude at about 50 km from the mouth. The lower panels relate to the current situation. In the course of the 20th century, and especially in the period 1970-1980, the morphology of the estuary was greatly changed by artificial interventions. The estuarine main channel was deepened, especially in the mouth zone, and fixed by submerged dikes. Large parts of the intertidal areas were diked and filled with dredged materials. Tidal damping and tidal distortion were greatly reduced. At present a small tidal bore occurs only under extreme tides and further inland than in the past.]]<br />
<br />
[[Image:ConvergingEstuarySchematization.jpg|right|450px|thumb|Figure 7. Schematization of a strongly converging estuary. (a) Plan view; (b) 3D view.]]<br />
<br />
As discussed before, the expansion of the tidal flood wave over large intertidal areas decreases its height and propagation speed. The opposite occurs when the tide propagates into a tidal channel that becomes progressively narrower in up-channel direction, see Fig. 7. Instead of expanding laterally, the tidal wave is contracted when propagating. In the hypothetical case of no friction, conservation of the tidal energy flux along the channel requires up-channel amplification of the tidal amplitude (according to Green's law<ref name=J>Jay, D.A. 1991. Green's law revisited: tidal long-wave propagation in channels with strong topography. J.Geophys.Res. 96: 20,585-20,598</ref>). Many estuaries with significant river inflow have an upstream converging channel. Intertidal areas are rather small, partly as a result of natural sedimentation but often also as a result of human reclamation. The channel depth along the thalweg is fairly uniform<ref name=Sa>Savenije, H.H.G. 2012. Salinity and Tides in Alluvial Estuaries, second ed., Salinity and Tides in Alluvial Estuaries, second ed., www.salinityandtides.com </ref>, but shoals may be present in the mouth zone. The uniformity of the depth can also be due to dredging works for navigation purposes. <br />
<br />
Insight in the role of the most important nonlinear terms can be gained when simplifications are made. In the following we consider an idealized estuary with exponentially converging width. The corresponding estuarine geometry is shown in Fig. 7. The mean water depth <math>h</math> is uniform throughout the estuary; the channel width <math>B</math> converges exponentially and the intertidal width <math>B_I</math> increases linearly from the LW level up to the HW level, <br />
<br />
<math>B_C = b_c e^{-x/L_b} , \; B_I = e^{-x/L_b} \Delta b (1 + \zeta / h), \; <b> = b_C+\Delta b. \quad \quad (12)</math><br />
<br />
It should be borne in mind that although many estuaries have an upstream converging width, the assumption of exponential width convergence and uniform depth is for most estuaries a very rough approximation. Often only a limited part of the estuary can be represented in this way. <br />
<br />
Tidal propagation in this part of the estuary can be described by the mass and momentum balance equations (5) and (6). The instantaneous local depth is <math>D(x,t)=h+\zeta(x,t)</math> and the cross-sectional averaged tidal velocity is <math>u(x,t)</math>. Density gradients are left out of consideration. When substituting the expressions (12) for the width and omitting all nonlinear terms we obtain<br />
<br />
<math> \Large \frac{<b>}{b_C} \frac{\partial \zeta}{\partial t}\normalsize + h \Large \frac{\partial u}{\partial x}\normalsize – u \Large \frac{h}{L_b} \normalsize = 0 . \quad \quad (13)</math><br />
<br />
<math>\Large\frac{\partial u}{\partial t}\normalsize + g \Large \frac{\partial \zeta}{\partial x}\normalsize + r \Large \frac{u}{h}\normalsize = 0 . \quad \quad (14)</math><br />
<br />
Solving these linear equations (only tide, no river discharge) yields <br />
<br />
<math>\zeta = a e^{-\mu x} \; cos(kx-\omega t) \quad </math> with <math>\quad 2 L_b \; \mu = \normalsize -1 + \Large[\normalsize 1 – (\Large \frac{1}{2} \normalsize + 2 K_0^2) +\large[\normalsize (\Large \frac{1}{2}\normalsize + 2 K_0^2 )^2+ 4 (K_c^2 - K_0^2) \large]^{\large 1/2} \Large]^{\large 1/2} \normalsize, \quad \quad (15)</math><br />
<br />
where <math>K_0 = \Large \frac{\omega L_b}{\sqrt{ghb_C/<b>}}\normalsize , \; K_c = \Large \frac{r \omega L_b^2<b>}{g h^2b_C} \normalsize </math>. The damping factor <math>\mu</math> is positive for large friction and large convergence length (<math>K_c >K_0</math>). However, for small friction and small convergence length (<math>K_c <K_0</math>) the damping factor is negative: the tide is amplified when propagating up-channel. Even in the case of strong friction, the tide is only slightly damped or even amplified if the convergence length <math>L_b</math> is sufficiently small. In cases where tidal damping dominates over the effect of channel convergence (large <math>L_b</math>), the relative tidal amplitude decreases along the estuary; tidal asymmetry then becomes less relevant for upstream sediment transport. As noted before, the friction factor <math>r</math> can vary greatly between estuaries because of salinity stratification and the type of bed sediments (coarse or muddy). <br />
<br />
The solution of the Eqs. (13) and (14) also yields an expression for the wave propagation velocity <math>c</math>:<br />
<br />
<math>c = \Large \frac{\omega}{k}\normalsize = 2 \omega L_b \Large[\normalsize - 1 + (\Large \frac{1}{2} \normalsize + 2 K_0^2) +\large[\normalsize (\Large \frac{1}{2}\normalsize + 2 K_0^2 )^2+ 4 [K_c^2 - K_0^2] \large]^{\large 1/2} \Large]^{\large -1/2}\normalsize . \quad \quad (16)</math><br />
<br />
<br />
The expressions (15) and (16) show that tidal wave propagation depends on only two parameters, <math> K_0</math> and <math> K_c </math>. The linear equations (13) and (14) do not describe tidal wave deformation; for this, nonlinear terms have to be included (<math>u \partial u /\partial x</math> and time varying water depth <math>h+\zeta</math> in Eq. (13) and <math>b \zeta \partial u / \partial x</math> in Eq. (14)). <br />
<br />
In strongly converging friction-dominated estuaries the nondimensional wave numbers <math> K_0</math> and <math> K_c </math> have similar order of magnitude (consider, for example, <math>r \approx</math> 0.003 m/s, and the typical geometries <math>\Delta b <<b_C</math>, convergence length <math>L_b \approx</math> 25 km and depth <math>h \approx</math> 8 m, or convergence length <math>L_b \approx</math> 10 km and depth <math>h \approx</math> 5 m). In this case <math>\mu \approx 0</math>: the longitudinal variation of the tidal amplitude is small. Although friction causes damping of the tidal amplitude along the estuary, observations show that the tidal amplitude in many estuaries is fairly uniform along the estuary (Friedrichs and Aubrey, 1994<ref name=Fr> Friedrichs C.T. and Aubrey, D.G. 1994. Tidal propagation in strongly convergent channels. J.Geophys.Res. 99: 3321-3336</ref>; Prandle, 2004<ref> Prandle, D. 2004. How tides and river flows determine estuarine bathymetries. Progress in Oceanography 61: 1–26</ref>; Savenije, 2012<ref name=Sa></ref> ); see also the article [[Physical processes and morphology of synchronous estuaries]]. The reason is that tidal amplification by the funneling effect approximately cancels tidal damping due to friction. In a strongly, exponentially converging estuary the tide is propagating upstream with a phase difference of approximately 90° between tidal elevation and tidal velocity (Jay, 1991<ref name=J></ref>). In some estuaries the funneling effect even produces an increase of the tidal amplitude in the strongly converging part of the estuary; examples are the [[Morphology of estuaries#Hooghly estuary|Hooghly]] (Fig. 1), [[Morphology of estuaries#Western Scheldt and Scheldt estuary|Scheldt]], Humber, Gironde-Garonne. <br />
<br />
In the case of strong friction and strong exponential width convergence, the tidal equations (5) and (6) can be simplified by neglecting the term <math>B_C \partial (Du) / \partial x</math> compared to <math>Du \partial B_C / \partial x</math> in Eq. (5) and the terms <math>\partial u / \partial t</math>, <math> u \partial u / \partial x</math> compared to <math>ru/h</math> in Eq. (6). The two simplified equations can be combined by eliminating <math>u</math>. This yields the simple characteristic equation<br />
<br />
<math>\Large\frac{d}{dt}\normalsize \zeta(x,t) = 0 , \quad \Large\frac{dx}{dt}\normalsize = c = \Large\frac{g b_C D^2}{r b_S L_b}\normalsize . \quad \quad (17)</math><br />
<br />
If the relative tidal amplitude <math>a/h</math> and the relative intertidal area <math>\Delta b / b_C</math> are small, the HW propagation velocity <math>c^+</math>, and LW propagation velocity <math>c^-</math> follow directly from Eq. (17): <br />
<br />
<math> c^{\pm} \approx \Large\frac{g b_C h^2}{r L_b <b>}\normalsize \; (1 \pm \Large\frac{2a}{h}\normalsize \mp \Large\frac{\Delta b}{<b>}\normalsize ) . \quad \quad (18)</math><br />
<br />
A similar expression was already obtained by Friedrichs and Aubrey (1994) <ref name=Fr></ref> from an analytical model of converging estuaries with small relative tidal amplitudes and small intertidal areas. The role of the nonlinear terms for tidal distortion is similar as for the prismatic channel. The nonlinearity in the friction term Eq. (7) implies less friction in the period around HW compared to the period around LW and a corresponding increase of the HW propagation speed compared to the LW propagation, yielding positive tidal asymmetry. The nonlinearity related to the width increase with rising water level Eq. (8) implies a decrease of the HW propagation velocity compared to the LW propagation, yielding negative tidal asymmetry.<br />
<br />
[[Image:CharenteSpringNeapTide.jpg|left|350px|thumb|Figure 8: Tidal elevation (solid) and current velocity (dotted) curves in the Charente estuary for springtide (red) and neap tide (blue). The spring tidal curves exhibit a steep tidal rise and flood currents that are stronger than ebb currents. Hardly any tidal asymmetry occurs during neap tide and ebb currents are stronger than flood currents. Data from Toublanc et al. (2015) <ref>Toublanc, F., Brenon, I., Coulombier, T. and LeMoine, O. 2015. Fortnightly tidal asymmetry inversions and perspectives on sediment dynamics in a macrotidal estuary (Charente, France). Continental Shelf Res. 94: 42–54</ref>. Characteristic parameters for the Charente estuary are: channel depth <math>h \approx</math> 6.5 m, convergence length <math>L_b \approx</math> 10 km.]]<br />
<br />
The examples of tidal propagation in a prismatic channel and tidal propagation in a strongly converging estuary show that strong positive tidal asymmetry will develop only in estuaries with a large relative tidal amplitude <math>a/h</math> and small relative intertidal area <math>\Delta b / b_C</math>. The analytic models can only be evaluated for small values of <math>a/h</math>. However, the physical mechanisms for the development of strong tidal asymmetry are basically the same when <math>a/h</math> is no longer a small quantity, as confirmed by fully nonlinear mathematical models (Peregrine, 1966<ref> Peregrine, D.H. 1966. Calculations of the development of an undular bore J. Fluid Mech. 25: 321–30</ref>; Filippini, 2019<ref> Filippini, A.G., Arpaia, L., Bonneton, P. and Ricchiuto, M. 2019. Modeling analysis of tidal bore formation in convergent estuaries. European Journal of Mechanics - B/Fluids 73: 55-68</ref>). The importance of the parameter <math>a/h</math> for the development of positive tidal asymmetry is illustrated by observations that show a positive tidal asymmetry at spring tide and a negative tidal asymmetry at neap tide in the Pungue estuary (Mozambique; Nzualo et al., 2018<ref> Nzualo, T.N.M., Gallo, M.N. and Vinzon, S.B. 2018. Short-term tidal asymmetry inversion in a macrotidal estuary (Beira, Mozambique). Geomorphology 308: 107–117</ref>) and the [[Morphology of estuaries#Charente estuary|Charente estuary]] (France; Toublanc et al., 2015<ref> Toublanc, F., Brenon, I., Coulombier, T. and LeMoine, O. 2015. Fortnightly tidal asymmetry inversions and perspectives on sediment dynamics in a macrotidal estuary (Charente,France). Continental Shelf Res. 94: 42–54</ref>). This is illustrated in Fig. 8 for the [[Morphology of estuaries#Charente estuary|Charente estuary]], by comparing the curves for tidal elevation and current velocity for springtide (large <math>a/h</math>) and neap tide (small <math>a/h</math>). During springtide the tidal rise is much steeper than for neap tide. The maximum flood current velocity is larger than the maximum ebb tidal velocity for springtide, while the opposite holds for neap tide. <br />
<br />
[[Image:TidalAsymmetryEstuaries.jpg|right|350px|thumb|Figure 9: The relative tidal amplitude <math>a/h</math> and corresponding relative difference between HW and LW propagation speed <math>\Delta c / c</math> for different estuaries, derived from tide gauge stations in the converging part of the estuary. Adapted from<ref name=Dr></ref>.]]<br />
<br />
In Fig. 9 the relative difference between HW and LW propagation speeds <math>\Delta c / c = 2(c^+ -c^-)/(c^++c^-)</math> are compared for estuaries with different relative tidal amplitude <math>a/h</math>. The figure shows a positive correlation between <math>\Delta c / c </math> and <math>a/h</math>. Although <math>a/h</math> is the most important parameter, other factors also influence the relation between <math>a/h</math> and <math>\Delta c / c</math>, such as <math>K_0</math> and <math>K_c</math> (representing depth <math>h</math>, convergence length <math>L_b</math> and friction parameter <math>r</math>), the relative intertidal area <math>\Delta b/b_C</math> and the mean river discharge <math>Q_R</math>. The dependence of <math>\Delta c / c </math> on <math>a/h</math> is therefore different for each estuary. <br />
<br />
Equation (18) yields an estimate for the location <math>x</math> where the high-water wave crest overtakes the low-water wave trough, assuming that the tide at the estuarine mouth (<math>x=0</math>) is approximately symmetric and assuming that Eq. (18) remains approximately valid in the strong nonlinear case. For an estuary with small intertidal areas the distance <math>x</math> is given by<br />
<br />
<math>x = \Large\frac{\pi}{4}\frac{gh^2}{\omega r L_b}\frac{h}{a}\normalsize . \quad \quad (19)</math><br />
<br />
For example, in the case of the Gironde-Garonne estuary and tidal river system (<math>a \approx 2.5 m, h \approx 8 m, L_b \approx 35 km, r \approx 0.0025 m/s</math>) we find <math>x \approx 130 </math> km from the estuarine mouth, which is close to the location where a tidal bore is often observed. This example shows that a tidal bore will form if (1) frictional damping of the tidal wave is compensated by the funneling effect of width convergence and (2) the distance over which the tide can propagate into the estuary is sufficiently long (see also the article [[Tidal bore dynamics]]). <br />
<br />
In estuaries where frictional damping is not compensated by the funneling effect of width convergence, tidal asymmetry is generated in a similar way by the nonlinear processes described above (Friedrichs and Madsen, 1992<ref> Friedrichs, C.T. and Madsen, O.S. 1992. Non-linear diffusion of the tidal signal in frictionally dominated embayments. J.Geophys.Res. 97: 5637-5650</ref>). However, reduction of the relative tidal amplitude <math>a/h</math> by damping of the tidal wave may prevent tidal bore development. <br />
<br />
<br />
==Morphology of estuaries with tidal rivers==<br />
<br />
In a converging (funnel-shaped) estuary with strong friction, the tidal velocity <math>u</math> is mainly determined by the water surface slope <math>\partial \zeta /\partial x</math>, according to Eq. 14. A short period of tidal rise compared to the period of tidal fall implies steeper water surface slopes during flood than during ebb, with maximum flow rates that are higher during flood than during ebb, as illustrated in Fig. 8. Therefore, sediment fluxes during flood tide are higher than sediment fluxes during ebb tide, resulting in a net import of sediment into the estuary. As shown before, flood dominance increases with increasing relative tidal amplitude <math>a/h</math>. The time span over which flood dominance develops also plays a role. For converging estuaries the relevant nondimensional time duration indicator is mainly determined by the ratio of convergence length and tide propagation speed <math>L_b \omega/ c</math>. The value of the nondimensional parameter <math>a L_b \omega / (h c)</math> can be considered an indication for the strength of flood dominance. <br />
<br />
[[Image:TidalAsymmetryRiverFlow.jpg|right|400px|thumb|Figure 10: Tidal asymmetry indicator versus river flow indicator for different estuaries. A positive correlation is an indication that river flow makes an important contribution to compensating for tide-induced sediment import. The spread in the data is related to many other factors that influence sediment import/export. Adapted from <ref name=D17>Dronkers, J. 2017. Convergence of estuarine channels. Continental Shelf Res. 144: 120–133</ref>.]]<br />
<br />
Infill of estuaries is limited by sediment export through river flow, although dredging may also play a role. The influence of river flow on sediment export can be represented by the nondimensional parameter <math>Q_R/Q_{tide}</math>, where <math>Q_R</math> is the mean river discharge and <math>Q_{tide}</math> the maximum tidal discharge in the mid-estuarine zone (<math>x \approx L_b/2</math>). For estuaries in morphological equilibrium, sediment import due to tidal asymmetry (flood dominance) should be approximately balanced by export due to river flow. Comparing different estuaries one may thus expect a positive correlation between the parameters <math>a L_b \omega / (h c)</math> and <math>Q_R/Q_{tide}</math> <ref name=D17></ref>. As shown in Fig. 10, such a positive correlation exists, although the spread in the data is large. This spread can be due to many other factors, which influence sediment import and export in different ways. Possible important factors are<ref name=Dr></ref>:<br />
* dredging,<br />
* import/export by [[Morphology of estuaries#Wave-dominated systems|wave activity]],<br />
* import by [[estuarine circulation]],<br />
* sediment recirculation in ebb/flood-channel cells,<br />
* sediment import/export related to settling and erosion time lags,<br />
* fluvial sediment supply,<br />
* type of [[Coastal and marine sediments|sediment]].<br />
<br />
<br />
==Related articles==<br />
:[[Morphology of estuaries]]<br />
:[[Ocean and shelf tides]]<br />
:[[Tidal bore dynamics]]<br />
:[[Tidal motion in shelf seas]]<br />
:[[Estuarine circulation]]<br />
<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
==Appendix A==<br />
<br />
The tidal equations (1,2) can be cast in the form of two characteristic equations<br />
<br />
<math>\Large\frac{d}{dt}\normalsize[u(x,t) - 2c(x,t)] = 0, \quad \Large\frac{dx}{dt}\normalsize = u(x,t) – c(x,t) , \quad \quad (A1)</math><br />
<br />
<math>\Large\frac{d}{dt}\normalsize[u(x,t) + 2c(x,t)] = 0, \quad \Large\frac{dx}{dt}\normalsize = u(x,t) + c(x,t) . \quad \quad (A2)</math><br />
<br />
According to Eq. (A1), <math>u(x,t)-2c(x,t) \approx u_0-2c_0</math>, where <math>u_0=u(0,0), \; c_0=\sqrt{gD(0,0).}</math> Substitution in Eq. (A2) then implies that <math>u+2c=4c-2c_0-u_0</math> propagates with velocity <math>u+c=3c-2c_0-u_0</math>:<br />
<br />
<math>\Large\frac{d}{dt}\normalsize (4c-2c_0-u_0) = 0, \quad \Large\frac{dx}{dt}\normalsize = 3c-2c_0-u_0 . \quad \quad (A3)</math><br />
<br />
Because <math>c_0, u_0</math> are constants, the same characteristic equation (A3) holds for <math>c=\sqrt{gD(x,t)}</math>, for <math>D(x,t)</math> and for <math>\zeta(x,t)</math>. Eq. (3) is the characteristic equation for <math>\zeta(x,t)</math>. <br />
<br />
==Appendix B==<br />
<br />
The solution of the first order linear equations (1) and (2) is <br />
<br />
<math>\zeta^{(1)}=a \cos \theta , \; u^{(1)} = \Large\frac{c_0}{h}\normalsize \zeta^{(1)} , \quad \quad (B1)</math> <br />
<br />
where <math>\theta= k_0 x-\omega t</math>, <math>\omega</math> is the M2 radial frequency, the wave number <math>k_0 = \Large \frac{\omega}{gh} \normalsize</math> and <math>c_0=\omega / k</math>. <br />
<br />
After substitution in the nonlinear terms we have a linear equation for the second order approximation. The solution is<br />
<br />
<math>\zeta = \zeta^{(1)} + \zeta^{(2)} , \quad \zeta^{(2)} = \Large \frac{3 a^2}{4h}\normalsize kx \sin 2 \theta . \quad \quad (B2)</math><br />
<br />
The location of the wave crest at time <math>t</math> is called <math>x^+(t) </math>. At this location the surface slope is zero:<br />
<br />
<math> \Large \frac{\partial \zeta}{\partial x}\normalsize (x^+(t),t) = -a k_0 \sin \theta^+ + \Large \frac{3 a^2}{4h}\normalsize k_0 [ \sin 2 \theta^+ + 2kx \cos 2 \theta^+ ] = 0 \quad </math> , with <math>\theta^+=k_0 x^+(t) - \omega t . \quad \quad (B3)</math><br />
<br />
Because <math>a/h</math> is small, the wave crest is at a location where <math>\theta^+</math> is small (<math>|\theta^+ |<<1</math>). An approximate expression for the location of the wave crest is then given by <br />
<br />
<math>x^+(t) \approx (1 - \Large \frac{3a}{2h}\normalsize)^{-1} c_0 t . \quad \quad (B4)</math>. <br />
<br />
The propagation speed of the HW wave crest (Eq. 4) follows from <math>c^+(t)=dx^+/dt</math>. <br />
<br />
The first order linear equations (9) and (10) can be solved by eliminating <math>u(x,t)</math>, yielding a diffusion equation for the tidal elevation <math>\zeta(x,t)</math>:<br />
<br />
<math>\Large\frac{\partial \zeta^{(1)} }{\partial t}\normalsize = \Large\frac{h^2}{r}\frac{B_C}{<B>}\frac{\partial^2 \zeta^{(1)} }{\partial x^2}\normalsize .\quad \quad (B5)</math><br />
<br />
The first order solution is<br />
<br />
<math>\zeta^{(1)} = \Large\frac{1}{2}\normalsize a e^{i (\kappa x - \omega t)} + c.c. </math>, <br />
where <math>c.c. </math> is the complex conjugate, <math>\kappa = k+i \mu , \; k = \mu = \sqrt { \Large \frac{\omega r}{2 g h^2}\normalsize }. \quad \quad (B6) </math><br />
<br />
After substitution in the nonlinear terms the second order linear equations can be solved, yielding<br />
<br />
<math>\zeta = \zeta^{(1)} + \zeta^{(2)} , \quad \zeta^{(2)} \approx a (\Large \frac{\Delta b}{8 B_C} - \frac{a}{2h}\normalsize) e^{-2i \omega t} (e^{2i \kappa x} -e^{\sqrt{2} i \kappa x} ) + \Large \frac{a^2}{4h}\normalsize (1 – e^{-2 \mu x}) + c.c. \quad \quad (B7)</math><br />
<br />
In the same way as before the location of the wave crest is derived from the condition <br />
<br />
<math> \Large \frac{\partial \zeta}{\partial x} \normalsize (x^+(t),t) =0</math> for <math>| k x^+ - \omega t|<< 1</math>. <br />
<br />
The propagation speed of the HW wave crest (Eq. 11) follows from <math>c^+(t)=dx^+/dt</math>; this expression holds for the lower portion of the estuary where <math>kx<<1</math>.<br />
<br />
<br />
<br />
<br />
{{2Authors<br />
|AuthorID1=120<br />
|AuthorFullName1=Job Dronkers<br />
|AuthorName1=Dronkers J<br />
|AuthorID2=15152<br />
|AuthorFullName2= Philippe Bonneton <br />
|AuthorName2= Bonneton P<br />
}}<br />
<br />
<br />
[[Category: Physical coastal and marine processes]]<br />
[[Category: Estuaries and tidal rivers]]<br />
[[Category: Morphodynamics]]<br />
[[Category:Hydrodynamics]]</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Tidal_asymmetry_and_tidal_basin_morphodynamics&diff=76282Tidal asymmetry and tidal basin morphodynamics2019-12-16T16:54:31Z<p>Dronkers J: </p>
<hr />
<div><br />
This article describes the physical processes responsible for tidal wave deformation in shallow coastal inlet systems – tidal lagoons and estuaries. A qualitative discussion is given of the mutual interaction between tidal asymmetry generation and morphological development of these systems, which is generally referred to by the term ''self-organizing morphodynamics''. This article is largely based on the book ''Dynamics of Coastal Systems'' <ref name=Dr>Dronkers, J. 2017. Dynamics of Coastal Systems. World Scientific Publ. Co, Singapore, 740 pp.</ref>. <br />
<br />
==Tidal wave deformation in shallow water==<br />
<br />
Tides result from the response of the ocean water bodies to the attractive gravitational forces by sun and moon. Tidal motion in the oceans can be described by a limited number of sinusoidal components, because earth's rotation and the relative movements of earth, sun and moon have a cyclical character, see the article [[Ocean and shelf tides]]. The semidiurnal lunar tide (M2) is usually the dominant component, in which case the ocean tide can be described fairly accurately with a single sine function.<br />
<br />
Ocean tidal waves are distorted when they propagate into shallow coastal waters. Here the term tidal wave distortion is to be understood as a systematic (long-term averaged) difference between the periods of rising and falling tide, also called tidal asymmetry. We will use the term positive duration asymmetry for tides with a longer fall and shorter rise and negative duration asymmetry for tides with a shorter fall and longer rise. Nonlinear hydrodynamic processes that are insignificant in the deep ocean become important when the tidal range is larger than a small fraction of the mean water depth. In the following we shortly review the major nonlinear processes involved in initiating shallow-water tidal distortion. <br />
<br />
However, it must be noted before that linear ocean tides are not fully symmetric, due to the superposition of certain tidal components with mutually related frequencies (for example, the sum of the frequencies of the K1 and O1 tides is equal to the frequency of the M2 tide). Although this was known for a long time (Doodson, 1921)<ref> Doodson, A.T. 1921. The harmonic development of the tide-generating potential. Proc.R.Soc.London, Ser.A 100: 305-329</ref>, it has received renewed attention more recently due to the observations and analyses of Hoitink et al. (2003)<ref> Hoitink, A.F.J., Hoekstra, P. and van Mare, D.S. 2003. Flow asymmetry associated with astronomical tides: Implications for residual transport of sediment. J.Geophys.Res. 108: 13-1 - 13-8</ref> and several other studies since (Nidzieko, 2010<ref>Nidzieko, J. 2010. Tidal asymmetry in estuaries with mixed semidiurnal/diurnal tides. J. Geophysical Research 115, C08006, doi:10.1029/2009JC005864</ref>; Zhang, 2018 <ref>Zhang, W., Cao, Y., Zhu, Y., Zheng, J., Ji, X., Xu, Y., Wu, Y. and Hoitink, A.F.J. 2018. Unravelling the causes of tidal asymmetry in deltas. Journal of Hydrology 564: 588–604</ref>). A world map showing ocean regions with [[Ocean and shelf tides#Asymmetric ocean tides|asymmetric tides]] was published by Song et al. (2011<ref> Song, D., X. H. Wang, A. E. Kiss, and Bao, X. 2011. The contribution to tidal asymmetry by different combinations of tidal constituents. J. Geophys. Res., 116, C12007</ref>), based on tidal constants derived from the TPXO7-ATLAS (http://volkov.oce.orst.edu/tides/atlas.html). Asymmetric tides (with either positive or negative duration asymmetry) occur mainly in regions where tides have a mixed character, with comparable magnitudes of diurnal and semidiurnal tidal components. <br />
<br />
Although the asymmetry of ocean tides can be significant, tidal asymmetry can become much stronger due to the generation of shallow-water overtides in shallow coastal areas with a large semidiurnal tidal range (dominated by M2). The distortion of the tide can be so strong that the durations of rising tide and falling tide become very different and that a large difference arises between the peak flow velocities of flood and ebb. Often the duration of rising tide is much shorter than the duration of falling tide. This is illustrated in Fig. 1 for the [[Morphology of estuaries#Hooghly estuary|Hooghly estuary]]. In the most extreme case, the duration of tidal rise becomes so short that a hydraulic jump develops at the front of the tidal wave. The front of the tidal wave appears as a propagating wall of water, a so-called tidal bore, as explained in the article [[Tidal bore dynamics]]. <br />
<br />
<br />
[[Image:HooghlyTidalWaveDeformation.jpg|center|700px|thumb|Figure 1: Tide curves in the Hooghly estuary observed during a high springtide (19/9/2009) at different tide gauges along the estuary. Data from Banerjee et al. (2015)<ref>Banerjee, A.P., Dutta, S. and Majumdar, A. 2015. Quest for the determination of environmental flow assessment for hilsa fish of the Hooghly estuary by hydraulic rating method. ARPN Journal of Engineering and Applied Sciences 10: 7885-7899</ref>]]<br />
<br />
<br />
We focus here on asymmetry generated by the interaction of tides with topographic characteristics. Most studies of overtide generation consider estuaries and tidal rivers with simple one-dimensional geometries. In these studies, the influence of channel curvature, secondary channels or local channel constrictions on tidal asymmetry are ignored. Asymmetries related to density gradients or wind-driven currents are also left out of consideration. <br />
<br />
<br />
==Tidal wave deformation in the absence of friction==<br />
<br />
The distortion of the tide described above is related to a difference in propagation speed of the high-water crest of the tidal wave and the low-water trough. This difference already occurs when the water depth below the wave crest is slightly greater than the water depth below the wave trough. This can be easily demonstrated for a tidal wave that propagates in <math>x</math>-direction with time <math>t</math> in deep water with little loss of friction. The most simple geometry is an infinite prismatic channel. The mean (tide-averaged) channel depth is called <math>h</math> (constant), the tidal elevation is called <math>\zeta(x,t)</math>, the total instantaneous water depth <math>D(x,t)=h+\zeta(x,t)</math> and the cross-sectionally averaged velocity <math>u(x,t)</math>. <br />
<br />
In the absence of friction, the tidal equations for mass and momentum read:<br />
<br />
<math>\Large\frac{\partial \zeta}{\partial t}\normalsize +\Large\frac{\partial(Du)}{\partial x}\normalsize=0 , \quad \quad (1)</math><br />
<br />
<math>\Large\frac{\partial u}{\partial t}\normalsize + u \Large\frac{\partial u}{\partial x} \normalsize + g \Large\frac{\partial \zeta}{\partial x}\normalsize = 0 , \quad \quad (2)</math><br />
<br />
where <math>g</math> is the gravitational acceleration. Overtides are due to the nonlinear terms <math>\partial(\zeta u) / \partial x </math> and <math> u \partial u / \partial x</math>. The quadratic nature of these terms implies that the first and most important overtide (M4) has twice the frequency of the M2 tide. The tidal equations (1,2) can be cast in the form of a characteristic equation that describes the propagation of the tidal wave <math>\zeta(x,t)</math> in positive x-direction,<br />
<br />
<math>\Large\frac{d}{dt}\normalsize \zeta(x,t) = 0 , \quad \Large\frac{dx}{dt}\normalsize = 3 c + u_0 – 2 c_0 , \quad \quad (3)</math><br />
<br />
where <math>c=\sqrt{gD(x,t)} , \; c_0= \sqrt{gD(0,0)} , \; u_0=u(0,0) .</math> A derivation is given in appendix A. We choose <math>x=0, t=0</math> at high water (HW) and assume that the relative tidal amplitude <math>a/h</math> during the time <math>t</math> remains small (<math> a/h << 1</math>). Then we have <math>D(0,0) \approx h+a , \; u(0,0) \approx a\sqrt{g/h}</math> as first-order solution of Eqs. (1) and (2). According to Eq. (3), HW thus propagates with velocity<br />
<br />
<math>c^+ = 3 c + u_0 – 2 c_0 = 3 \sqrt{g(h+a)} + a \sqrt{g/h} – 2 \sqrt{g(h+a)} \approx \sqrt{gh} (1 + \Large\frac{3a}{2h}\normalsize) . \quad \quad (4)</math><br />
<br />
<br />
[[Image:PropagatingWaveDeformation.jpg|right|400px|thumb|Figure 2: Deformation of a frictionless propagating wave. The blue curve is the sinusoidal tidal wave with amplitude <math>a</math> of 2 m, at <math>\small x=0</math>, <math>\small\zeta(x=0,t) = a \cos \omega t</math>. The red curve is the distorted tidal wave after travelling a distance of <math>\small x=</math> 100 km without friction in a channel of 10 m mean depth, according to the second-order solution of Eqs. (1) and (2) for <math>a/h<<1</math>, which is given by <math>\small \zeta(x,t) = \zeta^{(1)} + \zeta^{(2)} </math>, with <math>\small \zeta^{(1)} = a \cos(\omega t - kx)</math>, <math>\small\zeta^{(2)} = \large\frac{3 a^2}{4h} \small kx \sin(2 \omega t – 2kx) </math> (see appendix B). The dotted red line is the M4 overtide <math>\small \zeta^{(2)} </math>. The red curve displays a shorter tidal rise and a longer tidal fall: the tidal wave crest has propagated faster than the tidal wave trough.]]<br />
<br />
In the same way one finds for the propagation velocity of the low-water (LW) location <math>c^- \approx \sqrt{gh} (1 – \frac{3a}{2h})</math>. Another method to find this result is presented in appendix B. As HW propagates faster than LW, the tidal wave front will steepen progressively; the duration of rising tide shortens while the duration of falling tide is lengthened. This positive tidal asymmetry increases with the relative tidal amplitude <math>a/h</math> as a consequence of the nonlinear terms <math>\partial(\zeta u) / \partial x </math> and <math> u \partial u / \partial x</math> in the tidal equations. The resulting tidal distortion is illustrated in Fig. 2. Equation (4) suggests that after some time the high-water wave crest will overtake the low-water wave trough. However, this can only happen when the amplitude of the M4 overtide is of the same order of magnitude as the M2 tide, which violates the approximations used in Eq. (4).<br />
<br />
The tidal equations for a prismatic channel do not well represent tidal propagation in estuaries because of neglect of the friction term. The equations (1,2) are more representative for the [[Coriolis and tidal motion in shelf seas|along-shore propagation of a tidal Kelvin wave]], far away from hard boundaries where the tidal wave can reflect or from hydrodynamic boundaries where the Kelvin wave meets other tidal wave systems. An increasing tidal asymmetry develops in situations where the coastal zone is shallow and the tidal amplitude is large. The increasing tidal asymmetry along the coast of Normandy (France) can be understood in this way (Fig. 3), as well as the increasing tidal asymmetry along the North Sea coast of Holland (see: [[Coriolis and tidal motion in shelf seas]]). The tidal wave that enters estuaries situated along such coasts (the Seine at Le Havre, for instance) exhibits already significant positive-duration tidal asymmetry.<br />
<br />
<br />
[[Image:ChannelFrance.png|center|600px|thumb|Figure 3. Increasing positive asymmetry (<math>\Delta_{FR}</math> is the difference of the durations of tidal fall and tidal rise) of the tidal wave propagating along the coast of Normandy (France). Tide gauge data of 29 September 2015.]]<br />
<br />
<br />
==Tidal wave deformation in the presence of friction and intertidal areas==<br />
<br />
Tidal asymmetry develops during up-channel propagation into a shallow tidal basin. Pronounced tidal asymmetry (possibly leading to tidal bore formation) only occurs if during propagation a sufficiently large ratio <math>a/h</math> is maintained. In many cases this condition is not met, because the tidal amplitude decreases during propagation. The two main reasons for decrease of the tidal amplitude are: (1) tidal wave damping by friction and (2) lateral spreading of the flood tidal wave. These two nonlinear processes also influence the propagation of the high-water wave crest and the low-water wave trough. <br />
<br />
We consider a tidal basin where the longitudinal tidal flow <math>u(x,t)</math> is confined in a single tidal channel with depth <math>D(x,t)</math> and width <math>B_C(x)</math>. Flood water can spread over intertidal areas; the width of the intertidal area <math>B_I(x,t)</math> is a function of the water level <math>\zeta(x,t)</math>. The tidal propagation in this basin can be described by the mass and momentum balance equations<br />
<br />
<math>B \Large\frac{\partial \zeta}{\partial t}+\frac{\partial}{\partial x}\normalsize (B_C Du) = 0 , \quad \quad (5)</math><br />
<br />
<math>\Large\frac{\partial u}{\partial t}\normalsize + u \Large\frac{\partial u}{\partial x} \normalsize + g \Large\frac{\partial \zeta}{\partial x}\normalsize + F = 0 , \quad \quad (6)</math><br />
<br />
where <math>B= B_C+B_I </math> is the total surface width. The symbol <math>F</math> in Eq. (6) stands for the frictional momentum dissipation which is usually represented by a quadratic expression of the form <math>F= c_D \large\frac{|u|u}{D} </math>. Although it appears from detailed measurements that this expression is a rough approximation – the friction coefficient <math>c_D</math> is found to be variable both temporally and spatially (Lewis and Lewis, 1987<ref> Lewis, R. E., and Lewis, J. O. 1987. Shear-stress variations in an estuary. Estuarine Coastal Shelf Sci. 25: 621–635</ref>; Stacey and Ralston, 2005<ref name=SR> Stacey, M.T. and Ralston, D.K. 2005. The Scaling and Structure of the Estuarine Bottom Boundary Layer. J. Physical Oceanography 35: 55-71</ref>; Lefebvre et al., 2012<ref> Lefebvre, A., Ernstsen, V.B and Winter, C. 2012. Estimation of roughness lengths and flow separation over compound bedforms in a natural-tidal inlet. Continental Shelf Research 61–62: 98-111 </ref>) – we consider here a further approximation assuming that the quadratic dependence on <math>u</math> can be ignored: <math>F = r \large\frac{u}{D}</math>. Here, is <math>r</math> a constant friction coefficient with dimension [m/s] that relates momentum dissipation at the channel bed to the depth-averaged current velocity. Its value typically ranges between 0.001 - 0.004 m/s <ref name=Dr></ref>. The precise value of the friction coefficient for estuarine flow is generally not well known as it is influenced by many factors such as density stratification (lower friction), small bed forms (higher friction) and fluid mud layers (lower friction). The friction coefficient may even be different for ebb and flood because of differences in salinity stratification<ref name=SR></ref>. In most estuaries, the tidal discharge amplitude is much larger than the river discharge, which therefore does not strongly influence frictional dissipation in the absence of salinity stratification. In this case, the linearization of the friction term is a minor approximation compared to the uncertainty in the value of the friction coefficient.<br />
<br />
[[Image:PrismaticTidalFlatChannelNEW.jpg|right|300px|thumb|Figure 4: Prismatic estuarine channel with tidal flats.]]<br />
<br />
The tidal equations (5) and (6) are too complex for an analytic treatment in which tidal asymmetry is explicitly related to the nonlinear terms. An analytical solution of the tidal equations requires further approximations, by assuming that the contribution of nonlinear terms is relatively small and can be linearized (Lanzoni and Seminara, 1998<ref> Lanzoni, S. and Seminara, G. 1998. On tide propagation in convergent estuaries, J. Geophys. Res. 103: 30793–30812</ref>).<br />
<br />
Therefore we consider a prismatic tidal channel with a uniform mean depth <math>h</math> much larger than the tidal amplitude <math>a</math>, such that the friction term can be approximated by<br />
<br />
<math>F = r \Large\frac{u}{D}\normalsize =r \Large\frac{u(x,t)}{h+\zeta(x,t)}\normalsize \approx r\Large\frac{u(x,t)}{h}\normalsize (1 - \Large\frac{\zeta(x,t)}{h}\normalsize) . \quad \quad (7)</math> <br />
<br />
We further assume that the intertidal storage width <math>B_I</math> is much smaller than the channel width <math>B_C</math> and that it increases linearly with the water level <math>\zeta(x,t)</math> (see Fig. 4):<br />
<br />
<math>B_I = \Delta b (1 + \Large\frac{\zeta(x,t)}{h}\normalsize), \quad <B>=B_C+\Delta b . \quad \quad (8)</math> <br />
<br />
In shallow estuaries (<math>h \le 5 m</math>) with strong tides, the nondimensional friction coefficient <math>r / (h \omega)</math> is substantially larger than 1 (the symbol <math>\omega</math> is the M2 tidal frequency). In this case the inertial terms <math>\partial u / \partial x </math> and <math> u \partial u / \partial x</math> are much smaller than the friction term <math>F</math>.<br />
<br />
In prismatic well-mixed estuaries, where salinity stratification can be ignored and where frictional effects are much stronger than inertial effects, the one-dimensional cross-section-averaged tidal equations (5) and (6) for small values of <math>a/h</math> can be simplified to <br />
<br />
<math><B> \Large \frac{\partial \zeta}{\partial t} \normalsize + h B_C \Large \frac{\partial u}{\partial x}\normalsize + \Delta b \Large \frac{\zeta}{a} \frac{\partial \zeta}{\partial t} \normalsize + B_C \Large \frac{\partial (\zeta u)}{\partial x}\normalsize =0 , \quad \quad (9)</math><br />
<br />
<math>g\Large \frac{\partial \zeta}{\partial x}\normalsize + r \Large \frac{u}{h}\normalsize – r \Large \frac{u \zeta}{h^2}\normalsize =0 . \quad \quad (10)</math><br />
<br />
<br />
In such friction-dominated estuaries the tide does not travel as a propagating wave, but rather advances into the estuary through a diffusion-type process, as shown by Eq. (B5) and described by Blondeaux (1978) for the Saint Lawrence Estuary <ref name=LB> LeBlond, P. 1978. On tidal propagation in shallow rivers, J. Geophys. Res., 83: 4717–4721</ref>. The tidal wave crest does not coincide with the time of high water, but lags behind. The same applies to low water.<br />
<br />
The nonlinear terms in the tidal equations are much smaller than the linear terms if <math>\Delta b << B_C</math> and <math>a/h << 1</math>. In this case a first order solution <math>\zeta^{(1)}</math> can be found by substituting the solution of the linear equations in the nonlinear terms. The nonlinear terms then generate a small M4 tidal component <math>\zeta^{(2)}</math>, which affects the duration of tidal rise and tidal fall. This is because the propagation speed <math>c^+</math> of the high-water wave crest differs from the propagation speed <math>c^-</math> of the low-water wave trough (see appendix B):<br />
<br />
<math>c^{\pm} \approx [1 \pm (2 - \sqrt{2}) \Large\frac{a}{h}\normalsize \mp \Large\frac{\Delta b}{2B_C}\normalsize ] \; \sqrt{gh} \; \sqrt{ \Large\frac{2 \omega h}{r} \frac{B_C}{<B>}\normalsize} . \quad \quad (11) </math> <br />
<br />
where <math>\omega</math> is the M2 radial frequency. <br />
<br />
This expression exhibits the effect of other nonlinearities in tidal propagation than those considered in the example of the prismatic channel: the effect of intertidal areas in Eq. (9) and the effect of depth dependence of the friction term in Eq. (10). The nonlinearity in the friction term Eq. (7) implies less friction in the period around HW compared to the period around LW and a corresponding increase of the HW propagation speed compared to the LW propagation, yielding positive tidal asymmetry. The nonlinearity related to the width increase with rising water level represented by the third term in Eq. (9) implies a decrease of the HW propagation velocity compared to the LW propagation, yielding negative tidal asymmetry (Speer and Aubrey, 1985<ref> Speer, P.E. and Aubrey, D.G. 1985. A study of non-linear tidal propagation in shallow inlet/estuarine systems. Part II: theory. Estuarine, Coastal Shelf Sci. 21: 207-224</ref>). This is because the HW crest of the tidal wave is delayed when propagating into the estuary by diversion of flood water over the intertidal area, while the LW wave trough remains confined within the narrower channel when propagating into the estuary. Hence, shallowness of the channel (large <math>a/h</math>) and large intertidal area (large <math>\Delta b/B_C</math>) have counteracting effects on tidal wave distortion.<br />
<br />
==Morphology of shallow tidal basins with small river inflow==<br />
<br />
In the foregoing it was shown that the tidal wave that enters a shallow prismatic channel is distorted due to the opposite effects of friction and intertidal areas on the up-channel propagation of HW on the one hand and LW on the other. In short tidal basins, these effects are partially offset by the reflected tidal wave at the landward basin boundary<ref name=Dr></ref>. However, in the case of strong friction, the reflected tidal wave is much smaller than the incoming tidal wave in a large part of the basin. In this part of the tidal basin the tidal velocity <math>u</math> is mainly determined by the water surface slope <math>\partial \zeta /\partial x</math>, according to Eq. 10. A short period of tidal rise compared to the period of tidal fall implies steeper water surface slopes during flood than during ebb. Hence, maximum flood velocities are higher than maximum ebb velocities in the absence of significant river inflow. <br />
<br />
[[Image:EquilibriumTidalLagoonsNEW.jpg|right|500px|thumb|Figure 5: The relative tidal amplitude <math>a/h</math> versus the relative intertidal area <math>\Delta b/<B></math> for a large number of tidal basins with small (or without) river inflow. Many of these basins (but not all) are back-barrier tidal basins or tidal lagoons: basins that are semi-closed by a sand barrier at the entrance. The figure shows a positive correlation between <math>a/h</math> and <math>\Delta b/<B></math>. The correlation between these basin characteristics also depends on other parameters, in particular the tidal asymmetry already existing at the basin entrance, which is different for each basin. Therefore, one should not expect that all the point lie on a single line. Adapted from<ref name=Dr></ref>.]]<br />
<br />
Because the transported sediment load increases more than linearly with the current velocity (see the articles [[Sand transport]] and [[Sediment transport formulas for the coastal environment]]), sediment fluxes during flood tide are higher than sediment fluxes during ebb tide. Flood-dominant tidal asymmetry thus produces a net import of sediment into the basin. Sediment infill could possibly go on until no tidal basin is left. This has happened in the past to some tidal basins, but many tidal basins without river inflow still survive. The reason is that flood dominance is neutralized by several processes. One of these processes is wave action, which can suspend large amounts of sediment in the HW period that are subsequently transported out of the basin by ebb currents<ref>Friedrichs, C.T. 2011. Tidal Flat Morphodynamics: A Synthesis. In: Treatise on Estuarine and Coastal Science, vol. 3, Estuarine and Coastal Geology and Geomorphology. Ed.:J. D. Hansom and B. W. Fleming, Elsevier, Amsterdam: 137-170</ref><ref> Desguée, R., Robin, N., Gluard, L., Monfort, O., Anthony, E.J., Levoy, F. 2011. Contribution of hydrodynamic conditions during shallow water stages to the sediment balance on a tidal flat: Mont-Saint-Michel bay, Normandy, France. Estuarine<br />
Coastal Shelf Sci. 94: 343–354</ref>. However, tidal basins do not depend only on wave action for their survival. One reason is the so-called Stokes transport, the water outflow compensating for the net influx due to greater mean water depth during flood than during ebb. Another reason is the reduction of tidal asymmetry due to the presence of intertidal areas as discussed in the previous section. During the development of intertidal areas by flood-dominant sediment transport, tidal asymmetry is weakened until the average sediment transport by flood currents has become comparable to the average transport by ebb currents. In order to neutralize flood dominance with increasing relative tidal amplitude <math>a/h</math>, the counteracting effect of intertidal areas should also increase. Fig. 5 shows that this is indeed the case for natural tidal basins with small (or without) river inflow: tidal basins with larger relative tidal amplitude have larger intertidal areas. One may thus conclude that self-organizing processes can produce a natural equilibrium morphology for tidal basins in a sedimentary environment without geological constraints<ref name=Dr></ref> <ref>Dronkers, J. 1998. Morphodynamics of the Dutch Delta. In: Physics of estuaries and coastal seas. Ed.: J.Dronkers and M.B.A.M. Scheffers, Balkema, Rotterdam: 297-304</ref> (see also the article [[Morphology of estuaries]]). <br />
<br />
<br />
==Tidal wave deformation in a converging channel==<br />
<br />
The influence of friction on tidal propagation increases with decreasing depth. The LW propagation is slowed down more strongly than the HW propagation, which results in a larger tidal asymmetry. However, the tidal amplitude is decreased by frictional damping. During the past century many estuaries have been deepened for navigational purposes and intertidal areas have been reclaimed. The effect of these interventions on tidal propagation is illustrated in Fig. 6 for the Seine estuary and tidal river system. The tide propagates now much faster into the estuary and the tidal amplitude is much larger, especially in the upstream river. The tide propagation speed has increased more for the low waters than for the high waters, although the propagation of the high waters also benefits of the reduction of the intertidal areas. In the past a high tidal bore developed each spring tide in the downstream river. After the interventions (especially the dredging of the mouth bar) it takes a much larger distance before the HW wave crest overtakes the LW wave trough. A small tidal bore now develops far upstream and only for very high tidal coefficients<ref> Bonneton, N., Bonneton, P., Parisot, J-P., Sottolichio, A. and Detandt G. 2012. Tidal bore and Mascaret - example of Garonne and Seine Rivers. Comptes Rendus Geosciences, 344, 508-515</ref>. <br />
<br />
<br />
[[Image: SeineTidalDeformation.jpg|center|800px|thumb|Figure 6: Tidal wave distortion in the Seine estuary. The figures at the left show simultaneously recorded tide curves during springtide, for locations at various distances from the estuarine mouth. The images on the right show the morphology of the Seine estuary. The upper figures relate to the situation in the 19th century, when the morphology of the Seine estuary was almost in a natural state, with large shoals at the mouth (mouth bars) and an inner system with multiple channels and extensive intertidal areas. The 1876 tide curves (Comoy, 1881 <ref> Comoy, M. 1881. Etude pratique sur les marées fluviales. Gauthiers-Villars, Paris</ref>) display strong damping and delay in tidal propagation, especially for the low-waters. Tidal propagation over this complex shallow geometry resulted in a tidal bore that reached its largest amplitude at about 50 km from the mouth. The lower panels relate to the current situation. In the course of the 20th century, and especially in the period 1970-1980, the morphology of the estuary was greatly changed by artificial interventions. The estuarine main channel was deepened, especially in the mouth zone, and fixed by submerged dikes. Large parts of the intertidal areas were diked and filled with dredged materials. Tidal damping and tidal distortion were greatly reduced. At present a small tidal bore occurs only under extreme tides and further inland than in the past.]]<br />
<br />
[[Image:ConvergingEstuarySchematization.jpg|right|450px|thumb|Figure 7. Schematization of a strongly converging estuary. (a) Plan view; (b) 3D view.]]<br />
<br />
As discussed before, the expansion of the tidal flood wave over large intertidal areas decreases its height and propagation speed. The opposite occurs when the tide propagates into a tidal channel that becomes progressively narrower in up-channel direction, see Fig. 7. Instead of expanding laterally, the tidal wave is contracted when propagating. In the hypothetical case of no friction, conservation of the tidal energy flux along the channel requires up-channel amplification of the tidal amplitude (according to Green's law<ref name=J>Jay, D.A. 1991. Green's law revisited: tidal long-wave propagation in channels with strong topography. J.Geophys.Res. 96: 20,585-20,598</ref>). Many estuaries with significant river inflow have an upstream converging channel. Intertidal areas are rather small, partly as a result of natural sedimentation but often also as a result of human reclamation. The channel depth along the thalweg is fairly uniform<ref name=Sa>Savenije, H.H.G. 2012. Salinity and Tides in Alluvial Estuaries, second ed., Salinity and Tides in Alluvial Estuaries, second ed., www.salinityandtides.com </ref>, but shoals may be present in the mouth zone. The uniformity of the depth can also be due to dredging works for navigation purposes. <br />
<br />
Insight in the role of the most important nonlinear terms can be gained when simplifications are made. In the following we consider an idealized estuary with exponentially converging width. The corresponding estuarine geometry is shown in Fig. 7. The mean water depth <math>h</math> is uniform throughout the estuary; the channel width <math>B</math> converges exponentially and the intertidal width <math>B_I</math> increases linearly from the LW level up to the HW level, <br />
<br />
<math>B_C = b_c e^{-x/L_b} , \; B_I = e^{-x/L_b} \Delta b (1 + \zeta / h), \; <b> = b_C+\Delta b. \quad \quad (12)</math><br />
<br />
It should be borne in mind that although many estuaries have an upstream converging width, the assumption of exponential width convergence and uniform depth is for most estuaries a very rough approximation. Often only a limited part of the estuary can be represented in this way. <br />
<br />
Tidal propagation in this part of the estuary can be described by the mass and momentum balance equations (5) and (6). The instantaneous local depth is <math>D(x,t)=h+\zeta(x,t)</math> and the cross-sectional averaged tidal velocity is <math>u(x,t)</math>. Density gradients are left out of consideration. When substituting the expressions (12) for the width and omitting all nonlinear terms we obtain<br />
<br />
<math> \Large \frac{<b>}{b_C} \frac{\partial \zeta}{\partial t}\normalsize + h \Large \frac{\partial u}{\partial x}\normalsize – u \Large \frac{h}{L_b} \normalsize = 0 . \quad \quad (13)</math><br />
<br />
<math>\Large\frac{\partial u}{\partial t}\normalsize + g \Large \frac{\partial \zeta}{\partial x}\normalsize + r \Large \frac{u}{h}\normalsize = 0 . \quad \quad (14)</math><br />
<br />
Solving these linear equations (only tide, no river discharge) yields <br />
<br />
<math>\zeta = a e^{-\mu x} \; cos(kx-\omega t) \quad </math> with <math>\quad 2 L_b \; \mu = \normalsize -1 + \Large[\normalsize 1 – (\Large \frac{1}{2} \normalsize + 2 K_0^2) +\large[\normalsize (\Large \frac{1}{2}\normalsize + 2 K_0^2 )^2+ 4 (K_c^2 - K_0^2) \large]^{\large 1/2} \Large]^{\large 1/2} \normalsize, \quad \quad (15)</math><br />
<br />
where <math>K_0 = \Large \frac{\omega L_b}{\sqrt{ghb_C/<b>}}\normalsize , \; K_c = \Large \frac{r \omega L_b^2<b>}{g h^2b_C} \normalsize </math>. The damping factor <math>\mu</math> is positive for large friction and large convergence length (<math>K_c >K_0</math>). However, for small friction and small convergence length (<math>K_c <K_0</math>) the damping factor is negative: the tide is amplified when propagating up-channel. Even in the case of strong friction, the tide is only slightly damped or even amplified if the convergence length <math>L_b</math> is sufficiently small. In cases where tidal damping dominates over the effect of channel convergence (large <math>L_b</math>), the relative tidal amplitude decreases along the estuary; tidal asymmetry then becomes less relevant for upstream sediment transport. As noted before, the friction factor <math>r</math> can vary greatly between estuaries because of salinity stratification and the type of bed sediments (coarse or muddy). <br />
<br />
The solution of the Eqs. (13) and (14) also yields an expression for the wave propagation velocity <math>c</math>:<br />
<br />
<math>c = \Large \frac{\omega}{k}\normalsize = 2 \omega L_b \Large[\normalsize - 1 + (\Large \frac{1}{2} \normalsize + 2 K_0^2) +\large[\normalsize (\Large \frac{1}{2}\normalsize + 2 K_0^2 )^2+ 4 [K_c^2 - K_0^2] \large]^{\large 1/2} \Large]^{\large -1/2}\normalsize . \quad \quad (16)</math><br />
<br />
<br />
The expressions (15) and (16) show that tidal wave propagation depends on only two parameters, <math> K_0</math> and <math> K_c </math>. The linear equations (13) and (14) do not describe tidal wave deformation; for this, nonlinear terms have to be included (<math>u \partial u /\partial x</math> and time varying water depth <math>h+\zeta</math> in Eq. (13) and <math>b \zeta \partial u / \partial x</math> in Eq. (14)). <br />
<br />
In strongly converging friction-dominated estuaries the nondimensional wave numbers <math> K_0</math> and <math> K_c </math> have similar order of magnitude (consider, for example, <math>r \approx</math> 0.003 m/s, and the typical geometries <math>\Delta b <<b_C</math>, convergence length <math>L_b \approx</math> 25 km and depth <math>h \approx</math> 8 m, or convergence length <math>L_b \approx</math> 10 km and depth <math>h \approx</math> 5 m). In this case <math>\mu \approx 0</math>: the longitudinal variation of the tidal amplitude is small. Although friction causes damping of the tidal amplitude along the estuary, observations show that the tidal amplitude in many estuaries is fairly uniform along the estuary (Friedrichs and Aubrey, 1994<ref name=Fr> Friedrichs C.T. and Aubrey, D.G. 1994. Tidal propagation in strongly convergent channels. J.Geophys.Res. 99: 3321-3336</ref>; Prandle, 2004<ref> Prandle, D. 2004. How tides and river flows determine estuarine bathymetries. Progress in Oceanography 61: 1–26</ref>; Savenije, 2012<ref name=Sa></ref> ); see also the article [[Physical processes and morphology of synchronous estuaries]]. The reason is that tidal amplification by the funneling effect approximately cancels tidal damping due to friction. In a strongly, exponentially converging estuary the tide is propagating upstream with a phase difference of approximately 90° between tidal elevation and tidal velocity (Jay, 1991<ref name=J></ref>). In some estuaries the funneling effect even produces an increase of the tidal amplitude in the strongly converging part of the estuary; examples are the [[Morphology of estuaries#Hooghly estuary|Hooghly]] (Fig. 1), [[Morphology of estuaries#Western Scheldt and Scheldt estuary|Scheldt]], Humber, Gironde-Garonne. <br />
<br />
In the case of strong friction and strong exponential width convergence, the tidal equations (5) and (6) can be simplified by neglecting the term <math>B_C \partial (Du) / \partial x</math> compared to <math>Du \partial B_C / \partial x</math> in Eq. (5) and the terms <math>\partial u / \partial t</math>, <math> u \partial u / \partial x</math> compared to <math>ru/h</math> in Eq. (6). The two simplified equations can be combined by eliminating <math>u</math>. This yields the simple characteristic equation<br />
<br />
<math>\Large\frac{d}{dt}\normalsize \zeta(x,t) = 0 , \quad \Large\frac{dx}{dt}\normalsize = c = \Large\frac{g b_C D^2}{r b_S L_b}\normalsize . \quad \quad (17)</math><br />
<br />
If the relative tidal amplitude <math>a/h</math> and the relative intertidal area <math>\Delta b / b_C</math> are small, the HW propagation velocity <math>c^+</math>, and LW propagation velocity <math>c^-</math> follow directly from Eq. (17): <br />
<br />
<math> c^{\pm} \approx \Large\frac{g b_C h^2}{r L_b <b>}\normalsize \; (1 \pm \Large\frac{2a}{h}\normalsize \mp \Large\frac{\Delta b}{<b>}\normalsize ) . \quad \quad (18)</math><br />
<br />
A similar expression was already obtained by Friedrichs and Aubrey (1994) <ref name=Fr></ref> from an analytical model of converging estuaries with small relative tidal amplitudes and small intertidal areas. The role of the nonlinear terms for tidal distortion is similar as for the prismatic channel. The nonlinearity in the friction term Eq. (7) implies less friction in the period around HW compared to the period around LW and a corresponding increase of the HW propagation speed compared to the LW propagation, yielding positive tidal asymmetry. The nonlinearity related to the width increase with rising water level Eq. (8) implies a decrease of the HW propagation velocity compared to the LW propagation, yielding negative tidal asymmetry.<br />
<br />
[[Image:CharenteSpringNeapTide.jpg|left|350px|thumb|Figure 8: Tidal elevation (solid) and current velocity (dotted) curves in the Charente estuary for springtide (red) and neap tide (blue). The spring tidal curves exhibit a steep tidal rise and flood currents that are stronger than ebb currents. Hardly any tidal asymmetry occurs during neap tide and ebb currents are stronger than flood currents. Data from Toublanc et al. (2015) <ref>Toublanc, F., Brenon, I., Coulombier, T. and LeMoine, O. 2015. Fortnightly tidal asymmetry inversions and perspectives on sediment dynamics in a macrotidal estuary (Charente, France). Continental Shelf Res. 94: 42–54</ref>. Characteristic parameters for the Charente estuary are: channel depth <math>h \approx</math> 6.5 m, convergence length <math>L_b \approx</math> 10 km.]]<br />
<br />
The examples of tidal propagation in a prismatic channel and tidal propagation in a strongly converging estuary show that strong positive tidal asymmetry will develop only in estuaries with a large relative tidal amplitude <math>a/h</math> and small relative intertidal area <math>\Delta b / b_C</math>. The analytic models can only be evaluated for small values of <math>a/h</math>. However, the physical mechanisms for the development of strong tidal asymmetry are basically the same when <math>a/h</math> is no longer a small quantity, as confirmed by fully nonlinear mathematical models (Peregrine, 1966<ref> Peregrine, D.H. 1966. Calculations of the development of an undular bore J. Fluid Mech. 25: 321–30</ref>; Filippini, 2019<ref> Filippini, A.G., Arpaia, L., Bonneton, P. and Ricchiuto, M. 2019. Modeling analysis of tidal bore formation in convergent estuaries. European Journal of Mechanics - B/Fluids 73: 55-68</ref>). The importance of the parameter <math>a/h</math> for the development of positive tidal asymmetry is illustrated by observations that show a positive tidal asymmetry at spring tide and a negative tidal asymmetry at neap tide in the Pungue estuary (Mozambique; Nzualo et al., 2018<ref> Nzualo, T.N.M., Gallo, M.N. and Vinzon, S.B. 2018. Short-term tidal asymmetry inversion in a macrotidal estuary (Beira, Mozambique). Geomorphology 308: 107–117</ref>) and the [[Morphology of estuaries#Charente estuary|Charente estuary]] (France; Toublanc et al., 2015<ref> Toublanc, F., Brenon, I., Coulombier, T. and LeMoine, O. 2015. Fortnightly tidal asymmetry inversions and perspectives on sediment dynamics in a macrotidal estuary (Charente,France). Continental Shelf Res. 94: 42–54</ref>). This is illustrated in Fig. 8 for the [[Morphology of estuaries#Charente estuary|Charente estuary]], by comparing the curves for tidal elevation and current velocity for springtide (large <math>a/h</math>) and neap tide (small <math>a/h</math>). During springtide the tidal rise is much steeper than for neap tide. The maximum flood current velocity is larger than the maximum ebb tidal velocity for springtide, while the opposite holds for neap tide. <br />
<br />
[[Image:TidalAsymmetryEstuaries.jpg|right|350px|thumb|Figure 9: The relative tidal amplitude <math>a/h</math> and corresponding relative difference between HW and LW propagation speed <math>\Delta c / c</math> for different estuaries, derived from tide gauge stations in the converging part of the estuary. Adapted from<ref name=Dr></ref>.]]<br />
<br />
In Fig. 9 the relative difference between HW and LW propagation speeds <math>\Delta c / c = 2(c^+ -c^-)/(c^++c^-)</math> are compared for estuaries with different relative tidal amplitude <math>a/h</math>. The figure shows a positive correlation between <math>\Delta c / c </math> and <math>a/h</math>. Although <math>a/h</math> is the most important parameter, other factors also influence the relation between <math>a/h</math> and <math>\Delta c / c</math>, such as <math>K_0</math> and <math>K_c</math> (representing depth <math>h</math>, convergence length <math>L_b</math> and friction parameter <math>r</math>), the relative intertidal area <math>\Delta b/b_C</math> and the mean river discharge <math>Q_R</math>. The dependence of <math>\Delta c / c </math> on <math>a/h</math> is therefore different for each estuary. <br />
<br />
Equation (18) yields an estimate for the location <math>x</math> where the high-water wave crest overtakes the low-water wave trough, assuming that the tide at the estuarine mouth (<math>x=0</math>) is approximately symmetric and assuming that Eq. (18) remains approximately valid in the strong nonlinear case. For an estuary with small intertidal areas the distance <math>x</math> is given by<br />
<br />
<math>x = \Large\frac{\pi}{4}\frac{gh^2}{\omega r L_b}\frac{h}{a}\normalsize . \quad \quad (19)</math><br />
<br />
For example, in the case of the Gironde-Garonne estuary and tidal river system (<math>a \approx 2.5 m, h \approx 8 m, L_b \approx 35 km, r \approx 0.0025 m/s</math>) we find <math>x \approx 130 </math> km from the estuarine mouth, which is close to the location where a tidal bore is often observed. This example shows that a tidal bore will form if (1) frictional damping of the tidal wave is compensated by the funneling effect of width convergence and (2) the distance over which the tide can propagate into the estuary is sufficiently long (see also the article [[Tidal bore dynamics]]). <br />
<br />
In estuaries where frictional damping is not compensated by the funneling effect of width convergence, tidal asymmetry is generated in a similar way by the nonlinear processes described above (Friedrichs and Madsen, 1992<ref> Friedrichs, C.T. and Madsen, O.S. 1992. Non-linear diffusion of the tidal signal in frictionally dominated embayments. J.Geophys.Res. 97: 5637-5650</ref>). However, reduction of the relative tidal amplitude <math>a/h</math> by damping of the tidal wave may prevent tidal bore development. <br />
<br />
<br />
==Morphology of estuaries with tidal rivers==<br />
<br />
In a converging (funnel-shaped) estuary with strong friction, the tidal velocity <math>u</math> is mainly determined by the water surface slope <math>\partial \zeta /\partial x</math>, according to Eq. 14. A short period of tidal rise compared to the period of tidal fall implies steeper water surface slopes during flood than during ebb, with maximum flow rates that are higher during flood than during ebb, as illustrated in Fig. 8. Therefore, sediment fluxes during flood tide are higher than sediment fluxes during ebb tide, resulting in a net import of sediment into the estuary. As shown before, flood dominance increases with increasing relative tidal amplitude <math>a/h</math>. The time span over which flood dominance develops also plays a role. For converging estuaries the relevant nondimensional time duration indicator is mainly determined by the ratio of convergence length and tide propagation speed <math>L_b \omega/ c</math>. The value of the nondimensional parameter <math>a L_b \omega / (h c)</math> can be considered an indication for the strength of flood dominance. <br />
<br />
[[Image:TidalAsymmetryRiverFlow.jpg|right|400px|thumb|Figure 10: Tidal asymmetry indicator versus river flow indicator for different estuaries. A positive correlation is an indication that river flow makes an important contribution to compensating for tide-induced sediment import. The spread in the data is related to many other factors that influence sediment import/export. Adapted from <ref name=D17>Dronkers, J. 2017. Convergence of estuarine channels. Continental Shelf Res. 144: 120–133</ref>.]]<br />
<br />
Infill of estuaries is limited by sediment export through river flow, although dredging may also play a role. The influence of river flow on sediment export can be represented by the nondimensional parameter <math>Q_R/Q_{tide}</math>, where <math>Q_R</math> is the mean river discharge and <math>Q_{tide}</math> the maximum tidal discharge in the mid-estuarine zone (<math>x \approx L_b/2</math>). For estuaries in morphological equilibrium, sediment import due to tidal asymmetry (flood dominance) should be approximately balanced by export due to river flow. Comparing different estuaries one may thus expect a positive correlation between the parameters <math>a L_b \omega / (h c)</math> and <math>Q_R/Q_{tide}</math> <ref name=D17></ref>. As shown in Fig. 10, such a positive correlation exists, although the spread in the data is large. This spread can be due to many other factors, which influence sediment import and export in different ways. Possible important factors are<ref name=Dr></ref>:<br />
* dredging,<br />
* import/export by [[Morphology of estuaries#Wave-dominated systems|wave activity]],<br />
* import by [[estuarine circulation]],<br />
* sediment recirculation in ebb/flood-channel cells,<br />
* sediment import/export related to settling and erosion time lags,<br />
* fluvial sediment supply,<br />
* type of [[Coastal and marine sediments|sediment]].<br />
<br />
<br />
==Related articles==<br />
:[[Morphology of estuaries]]<br />
:[[Ocean and shelf tides]]<br />
:[[Tidal bore dynamics]]<br />
:[[Tidal motion in shelf seas]]<br />
:[[Estuarine circulation]]<br />
<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
==Appendix A==<br />
<br />
The tidal equations (1,2) can be cast in the form of two characteristic equations<br />
<br />
<math>\Large\frac{d}{dt}\normalsize[u(x,t) - 2c(x,t)] = 0, \quad \Large\frac{dx}{dt}\normalsize = u(x,t) – c(x,t) , \quad \quad (A1)</math><br />
<br />
<math>\Large\frac{d}{dt}\normalsize[u(x,t) + 2c(x,t)] = 0, \quad \Large\frac{dx}{dt}\normalsize = u(x,t) + c(x,t) . \quad \quad (A2)</math><br />
<br />
According to Eq. (A1), <math>u(x,t)-2c(x,t) \approx u_0-2c_0</math>, where <math>u_0=u(0,0), \; c_0=\sqrt{gD(0,0).}</math> Substitution in Eq. (B2) then implies that <math>u+2c=4c-2c_0-u_0</math> propagates with velocity <math>u+c=3c-2c_0-u_0</math>:<br />
<br />
<math>\Large\frac{d}{dt}\normalsize (4c-2c_0-u_0) = 0, \quad \Large\frac{dx}{dt}\normalsize = 3c-2c_0-u_0 . \quad \quad (A3)</math><br />
<br />
Because <math>c_0, u_0</math> are constants, the same characteristic equation (A3) holds for <math>c=\sqrt{gD(x,t)}</math>, for <math>D(x,t)</math> and for <math>\zeta(x,t)</math>. Eq. (3) is the characteristic equation for <math>\zeta(x,t)</math>. <br />
<br />
==Appendix B==<br />
<br />
The solution of the first order linear equations (1) and (2) is <br />
<br />
<math>\zeta^{(1)}=a \cos \theta , \; u^{(1)} = \Large\frac{c_0}{h}\normalsize \zeta^{(1)} , \quad \quad (B1)</math> <br />
<br />
where <math>\theta= k_0 x-\omega t</math>, <math>\omega</math> is the M2 radial frequency, the wave number <math>k_0 = \Large \frac{\omega}{gh} \normalsize</math> and <math>c_0=\omega / k</math>. <br />
<br />
After substitution in the nonlinear terms we have a linear equation for the second order approximation. The solution is<br />
<br />
<math>\zeta = \zeta^{(1)} + \zeta^{(2)} , \quad \zeta^{(2)} = \Large \frac{3 a^2}{4h}\normalsize kx \sin 2 \theta . \quad \quad (B2)</math><br />
<br />
The location of the wave crest at time <math>t</math> is called <math>x^+(t) </math>. At this location the surface slope is zero:<br />
<br />
<math> \Large \frac{\partial \zeta}{\partial x}\normalsize (x^+(t),t) = -a k_0 \sin \theta^+ + \Large \frac{3 a^2}{4h}\normalsize k_0 [ \sin 2 \theta^+ + 2kx \cos 2 \theta^+ ] = 0 \quad </math> , with <math>\theta^+=k_0 x^+(t) - \omega t . \quad \quad (B3)</math><br />
<br />
Because <math>a/h</math> is small, the wave crest is at a location where <math>\theta^+</math> is small (<math>|\theta^+ |<<1</math>). An approximate expression for the location of the wave crest is then given by <br />
<br />
<math>x^+(t) \approx (1 - \Large \frac{3a}{2h}\normalsize)^{-1} c_0 t . \quad \quad (B4)</math>. <br />
<br />
The propagation speed of the HW wave crest (Eq. 4) follows from <math>c^+(t)=dx^+/dt</math>. <br />
<br />
The first order linear equations (9) and (10) can be solved by eliminating <math>u(x,t)</math>, yielding a diffusion equation for the tidal elevation <math>\zeta(x,t)</math>:<br />
<br />
<math>\Large\frac{\partial \zeta^{(1)} }{\partial t}\normalsize = \Large\frac{h^2}{r}\frac{B_C}{<B>}\frac{\partial^2 \zeta^{(1)} }{\partial x^2}\normalsize .\quad \quad (B5)</math><br />
<br />
The first order solution is<br />
<br />
<math>\zeta^{(1)} = \Large\frac{1}{2}\normalsize a e^{i (\kappa x - \omega t)} + c.c. </math>, <br />
where <math>c.c. </math> is the complex conjugate, <math>\kappa = k+i \mu , \; k = \mu = \sqrt { \Large \frac{\omega r}{2 g h^2}\normalsize }. \quad \quad (B6) </math><br />
<br />
After substitution in the nonlinear terms the second order linear equations can be solved, yielding<br />
<br />
<math>\zeta = \zeta^{(1)} + \zeta^{(2)} , \quad \zeta^{(2)} \approx a (\Large \frac{\Delta b}{8 B_C} - \frac{a}{2h}\normalsize) e^{-2i \omega t} (e^{2i \kappa x} -e^{\sqrt{2} i \kappa x} ) + \Large \frac{a^2}{4h}\normalsize (1 – e^{-2 \mu x}) + c.c. \quad \quad (B7)</math><br />
<br />
In the same way as before the location of the wave crest is derived from the condition <br />
<br />
<math> \Large \frac{\partial \zeta}{\partial x} \normalsize (x^+(t),t) =0</math> for <math>| k x^+ - \omega t|<< 1</math>. <br />
<br />
The propagation speed of the HW wave crest (Eq. 11) follows from <math>c^+(t)=dx^+/dt</math>; this expression holds for the lower portion of the estuary where <math>kx<<1</math>.<br />
<br />
<br />
<br />
<br />
{{2Authors<br />
|AuthorID1=120<br />
|AuthorFullName1=Job Dronkers<br />
|AuthorName1=Dronkers J<br />
|AuthorID2=15152<br />
|AuthorFullName2= Philippe Bonneton <br />
|AuthorName2= Bonneton P<br />
}}<br />
<br />
<br />
[[Category: Physical coastal and marine processes]]<br />
[[Category: Estuaries and tidal rivers]]<br />
[[Category: Morphodynamics]]<br />
[[Category:Hydrodynamics]]</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Decision_support_tools&diff=76281Decision support tools2019-12-16T15:15:53Z<p>Dronkers J: </p>
<hr />
<div>A look at the '''decision support tools''' and their component parts that are available to decision makers and policy makers.<br />
<br />
==Terminology==<br />
The terms '''Decision Support Tools''' or '''Decision Support Systems (DSS)''' refer to a wide range of computer-based tools (simulation models, and/or techniques and methods) developed to support decision analysis and participatory processes. A DSS consists of a database, different coupled hydrodynamic and socio-economic models and is provided with a dedicated interface in order to be directly and more easily accessible by non-specialists (e.g. policy and decision makers). DSS have specific simulation and prediction capabilities but are also used as a vehicle of communication, training and experimentation <ref>Welp M. (2001). The use of decision support tools in participatory river basin management. ''Physics and Chemistry of the Earth, Part B: Hydrology, Oceans and Atmosphere'', '''26''' 7-8, 535-539.</ref>. Principally, DSS can facilitate dialogue and exchange of information thus providing insights to non-experts and support them in the exploration of policy options.<br />
<br />
==DSS Components==<br />
'''A Database Management System (DBMS)''': a DBMS collects, organizes, and processes data and information. <br />
<br />
'''Models''': different hydrodynamic and socio-economic models are integrated in a DSS to perform optimization, forecasting/prediction, statistical functions. The type of models included defines the type of support provided and the area of application of a DSS (i.e. [[erosion]] or shoreline management, [[pollution]], etc.). <br />
<br />
'''Users’ interface''': helps the users to interact with the system and to analyse its results. Important features of a DSS interface should be its user friendliness meaning its simplicity, flexibility, and capability of presenting data and model output. An effective user’s interface facilitates the communication and increases the acceptability of the tool by intended users (e.g. Coastal Zone Managers as well as Policy and Decision Makers).<br />
<br />
'''Other components''': [[GIS|Geographic Information Systems]] (GIS) play a significant role in ''Spatial Decision support systems'' (SDSS) in which they organise, present and compare data and information on a visualisation map; ''Web-Based DSS'' which are computerised systems that deliver decision support information to managers using a Web browser <ref>Bhargava H. K., D. J. Power and D. Sun (2007). Progress in Web-based decision support technologies. ''Decision Support Systems'', '''43''' 4, 1083.</ref>, ''Group Decision Support System (GDSS)'' are common computer tools or networks used to enable collaboration between people to solve complex decision making; <br />
<br />
==DSS Classification==<br />
See Power (2003)<ref name="Power">Power D. J. (2003). A Brief History of Decision Support Systems DSS. Resources.COM, World Wide Web, version 2.8, May 31, 2003.</ref><br />
<br />
* '''model-driven DSS''' emphasizes access to and manipulation of a statistical, financial, optimization, or simulation model. Model-driven DSS use data and parameters provided by users to assist decision makers in analyzing a situation; they are not necessarily data intensive.<br />
<br />
* '''communication-driven DSS''' supports more than one person working on a shared task. <br />
<br />
* '''data-driven DSS''' or data-oriented DSS emphasizes access to and manipulation of a time series of internal company data and, sometimes, external data.<br />
<br />
* '''document-driven DSS''' manages, retrieves and manipulates unstructured information in a variety of electronic formats.<br />
<br />
* '''knowledge-driven DSS''' provides specialized problem solving expertise stored as facts, rules, procedures, or in similar structures.<br />
<br />
==Practical application==<br />
The '''database management system''' component allows the organisation, facilitates access to and the elaboration of time series of raw data. <br />
* The '''integration''' of different type of knowledge (e.g. local and expert knowledge), disciplines and perspectives in the development of effective and sustainable water policies can find extremely useful support by the participatory development and implementation of DSS; <br />
* DSS helps multidisciplinary team involved in the analysis of a water problem to establish a ''common language'' and think in a structured way. Criteria, objectives and constraints about the problem become more explicit through the whole process of development and application of a decision support system. <br />
* The graphical features of a DSS '''support communication''' between stakeholders with different backgrounds. Visual aids in DSS also become more and more important when audiences are composed not only by policy makers but also by citizens. <br />
* Communication capabilities help in '''fostering public participation''' are particularly developed in Deliberation Support Tools. For instance Group Decision Support Systems support collaborative decision making;<br />
* '''Optimisation and simulation capabilities''' of the integrated help in the analysis of possible trade-offs and conflict situation for the identification of the most suitable within a set of alternative options integrated in the DSS help through the development of “''What if…?''” ''scenarios''.<br />
<br />
Specific techniques can be integrated in DSS to help for the selection (“''What is best/ what is good enough …?''”). For instance '''multi-criteria decision making''' for the [[evaluation]], benchmarking and raking of the different options identified. Optimisations models integrated in the systems help to identify the best between the generated alternatives.<br />
<br />
The use of [[GIS]] in '''Spatial Decision Support Systems''' allows for the definition hydrological and socio-economic maps that help in the multi-criteria analysis of the problem at hand. [[GIS]] components helps in the visualisation of the location of measures and impacts and facilitate the problem assessment by providing important information for the allocation of water management infrastructures. <br />
<br />
A DSS help in ''documenting'' the decision process that leads to the choice of a particular option thus contributes to its increasing transparency and fairness.<br />
In particular, COASTAL ZONE MANAGEMENT DSS are developed to help in the investigation of existing gaps on physical processes in coastal zones and their relationships to socio-economic demands and needs. They also support:<br />
<br />
* Water quality management (i.e. [[pollution]] control strategies, [[eutrophication]] management, salt intrusion and surface water quality). <br />
<br />
* Erosion management: management of dams and reservoirs operation and forecasting. <br />
<br />
* Identification of the location of physical structures (water treatment plants; dams; weirs; uptakes; monitoring stations; ...). <br />
<br />
* Risk assessment: flood forecasting, travel-time computations in Early-warning systems in the event of accidental [[pollution]]. Floods and drought management under scenarios of [[climate change]]. Drought mitigation measures during planning and operation of water systems.<br />
<br />
* Enforcement of laws (i.e. the [[Water Framework Directive]] – WFD): specifically tailored DSS can help with the implementation of water legislation and guide stakeholders to check on the authority’s performance and agenda management. <br />
<br />
* Assessment of the cost-effectiveness, the possible social impacts of the alternatives considered as well as the sustainability of water management measures. <br />
<br />
In the [[Stakeholder analysis]] section, the ''Quasta'' tool is described. This tool can be considered as a qualitative decision support tool, aimed to involve stakeholders in a decision-making process. It is not an optimisation tool, but has a rather deliberative design.<br />
<br />
==Links to web resources== <br />
* '''mDSS''' (Multi-sectoral Integrated and Operational decision support system for sustainable use of water resources at the catchment scale) - MULINO EU project <br />
<br />
: http://www.netsymod.eu/mDSS/<br />
<br />
* '''OPTIMA DSS''' (Optimisation for Sustainable Water Management) - OPTMA EU project <br />
<br />
: http://www.ess.co.at/OPTIMA/<br />
<br />
* '''WMSS''' (Water Management Support System) Integrated and problem oriented water management system at catchment scale for coastal water resources. - MEDITATE EU project <br />
<br />
: http://www.meditate.hacettepe.edu.tr/prjdesc/objectives.htm<br />
<br />
* '''SPICOSA SAF''' (System Approach Framework) A self-evolving, operational research approach framework for the assessment of policy options for the sustainable management of coastal zone systems. <br />
<br />
: http://www.spicosa.eu/<br />
<br />
<br />
==See also==<br />
:[[Decision Support Systems for coastal risk assessment and management]]<br />
:[[Policy instruments for integrated coastal zone management]]<br />
:[[Multicriteria techniques]]<br />
:[[Policy instruments for integrated coastal zone management]]<br />
:[[Input-output matrix]]<br />
<br />
<br />
<br />
==References==<br />
<references/><br />
<br />
This a revised extract from the Nostrum DSS Guidelines. Please refer to the Nostrum DSS Guidelines for a complete overview.<br />
http://www.feem-web.it/nostrum/doc/d5-2.pdf<br />
<br />
<br />
{{author<br />
|AuthorID=12523<br />
|AuthorName=Margaretha<br />
|AuthorFullName=Margaretha Breil}}<br />
<br />
[[Category:Integrated coastal zone management]]</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Decision_support_tools&diff=76280Decision support tools2019-12-16T15:05:02Z<p>Dronkers J: </p>
<hr />
<div>A look at the '''decision support tools''' and their component parts that are available to decision makers and policy makers.<br />
<br />
==Terminology==<br />
The terms '''Decision Support Tools''' or '''Decision Support Systems (DSS)''' refer to a wide range of computer-based tools (simulation models, and/or techniques and methods) developed to support decision analysis and participatory processes. A DSS consists of a database, different coupled hydrodynamic and socio-economic models and is provided with a dedicated interface in order to be directly and more easily accessible by non-specialists (e.g. policy and decision makers). DSS have specific simulation and prediction capabilities but are also used as a vehicle of communication, training and experimentation <ref>Welp M. (2001). The use of decision support tools in participatory river basin management. ''Physics and Chemistry of the Earth, Part B: Hydrology, Oceans and Atmosphere'', '''26''' 7-8, 535-539.</ref>. Principally, DSS can facilitate dialogue and exchange of information thus providing insights to non-experts and support them in the exploration of policy options.<br />
<br />
==DSS Components==<br />
'''A Database Management System (DBMS)''': a DBMS collects, organizes, and processes data and information. <br />
<br />
'''Models''': different hydrodynamic and socio-economic models are integrated in a DSS to perform optimization, forecasting/prediction, statistical functions. The type of models included defines the type of support provided and the area of application of a DSS (i.e. [[erosion]] or shoreline management, [[pollution]], etc.). <br />
<br />
'''Users’ interface''': helps the users to interact with the system and to analyse its results. Important features of a DSS interface should be its user friendliness meaning its simplicity, flexibility, and capability of presenting data and model output. An effective user’s interface facilitates the communication and increases the acceptability of the tool by intended users (e.g. Coastal Zone Managers as well as Policy and Decision Makers).<br />
<br />
'''Other components''': [[GIS|Geographic Information Systems]] (GIS) play a significant role in ''Spatial Decision support systems'' (SDSS) in which they organise, present and compare data and information on a visualisation map; ''Web-Based DSS'' which are computerised systems that deliver decision support information to managers using a Web browser <ref>Bhargava H. K., D. J. Power and D. Sun (2007). Progress in Web-based decision support technologies. ''Decision Support Systems'', '''43''' 4, 1083.</ref>, ''Group Decision Support System (GDSS)'' are common computer tools or networks used to enable collaboration between people to solve complex decision making; <br />
<br />
==DSS Classification==<br />
See Power (2003)<ref name="Power">Power D. J. (2003). A Brief History of Decision Support Systems DSS. Resources.COM, World Wide Web, version 2.8, May 31, 2003.</ref><br />
<br />
* '''model-driven DSS''' emphasizes access to and manipulation of a statistical, financial, optimization, or simulation model. Model-driven DSS use data and parameters provided by users to assist decision makers in analyzing a situation; they are not necessarily data intensive.<br />
<br />
* '''communication-driven DSS''' supports more than one person working on a shared task. <br />
<br />
* '''data-driven DSS''' or data-oriented DSS emphasizes access to and manipulation of a time series of internal company data and, sometimes, external data.<br />
<br />
* '''document-driven DSS''' manages, retrieves and manipulates unstructured information in a variety of electronic formats.<br />
<br />
* '''knowledge-driven DSS''' provides specialized problem solving expertise stored as facts, rules, procedures, or in similar structures.<br />
<br />
==Practical application==<br />
The '''database management system''' component allows the organisation, facilitates access to and the elaboration of time series of raw data. <br />
* The '''integration''' of different type of knowledge (e.g. local and expert knowledge), disciplines and perspectives in the development of effective and sustainable water policies can find extremely useful support by the participatory development and implementation of DSS; <br />
* DSS helps multidisciplinary team involved in the analysis of a water problem to establish a ''common language'' and think in a structured way. Criteria, objectives and constraints about the problem become more explicit through the whole process of development and application of a decision support system. <br />
* The graphical features of a DSS '''support communication''' between stakeholders with different backgrounds. Visual aids in DSS also become more and more important when audiences are composed not only by policy makers but also by citizens. <br />
* Communication capabilities help in '''fostering public participation''' are particularly developed in Deliberation Support Tools. For instance Group Decision Support Systems support collaborative decision making;<br />
* '''Optimisation and simulation capabilities''' of the integrated help in the analysis of possible trade-offs and conflict situation for the identification of the most suitable within a set of alternative options integrated in the DSS help through the development of “''What if…?''” ''scenarios''.<br />
<br />
Specific techniques can be integrated in DSS to help for the selection (“''What is best/ what is good enough …?''”). For instance '''multi-criteria decision making''' for the [[evaluation]], benchmarking and raking of the different options identified. Optimisations models integrated in the systems help to identify the best between the generated alternatives.<br />
<br />
The use of [[GIS]] in '''Spatial Decision Support Systems''' allows for the definition hydrological and socio-economic maps that help in the multi-criteria analysis of the problem at hand. [[GIS]] components helps in the visualisation of the location of measures and impacts and facilitate the problem assessment by providing important information for the allocation of water management infrastructures. <br />
<br />
A DSS help in ''documenting'' the decision process that leads to the choice of a particular option thus contributes to its increasing transparency and fairness.<br />
In particular, COASTAL ZONE MANAGEMENT DSS are developed to help in the investigation of existing gaps on physical processes in coastal zones and their relationships to socio-economic demands and needs. They also support:<br />
<br />
* Water quality management (i.e. [[pollution]] control strategies, [[eutrophication]] management, salt intrusion and surface water quality). <br />
<br />
* Erosion management: management of dams and reservoirs operation and forecasting. <br />
<br />
* Identification of the location of physical structures (water treatment plants; dams; weirs; uptakes; monitoring stations; ...). <br />
<br />
* Risk assessment: flood forecasting, travel-time computations in Early-warning systems in the event of accidental [[pollution]]. Floods and drought management under scenarios of [[climate change]]. Drought mitigation measures during planning and operation of water systems.<br />
<br />
* Enforcement of laws (i.e. the [[Water Framework Directive]] – WFD): specifically tailored DSS can help with the implementation of water legislation and guide stakeholders to check on the authority’s performance and agenda management. <br />
<br />
* Assessment of the cost-effectiveness, the possible social impacts of the alternatives considered as well as the sustainability of water management measures. <br />
<br />
In the [[Stakeholder analysis]] section, the ''Quasta'' tool is described. This tool can be considered as a qualitative decision support tool, aimed to involve stakeholders in a decision-making process. It is not an optimisation tool, but has a rather deliberative design.<br />
<br />
==Links to web resources== <br />
* '''mDSS''' (Multi-sectoral Integrated and Operational decision support system for sustainable use of water resources at the catchment scale) - MULINO EU project <br />
<br />
: http://www.netsymod.eu/mDSS/<br />
<br />
* '''OPTIMA DSS''' (Optimisation for Sustainable Water Management) - OPTMA EU project <br />
<br />
: http://www.ess.co.at/OPTIMA/<br />
<br />
* '''WMSS''' (Water Management Support System) Integrated and problem oriented water management system at catchment scale for coastal water resources. - MEDITATE EU project <br />
<br />
: http://www.meditate.hacettepe.edu.tr/prjdesc/objectives.htm<br />
<br />
* '''SPICOSA SAF''' (System Approach Framework) A self-evolving, operational research approach framework for the assessment of policy options for the sustainable management of coastal zone systems. <br />
<br />
: http://www.spicosa.eu/<br />
<br />
<br />
==See also==<br />
:[[Decision Support Systems for coastal risk assessment and management]]<br />
:[[Policy instruments for integrated coastal zone management]]<br />
<br />
<br />
==References==<br />
<references/><br />
<br />
This a revised extract from the Nostrum DSS Guidelines. Please refer to the Nostrum DSS Guidelines for a complete overview.<br />
http://www.feem-web.it/nostrum/doc/d5-2.pdf<br />
<br />
<br />
{{author<br />
|AuthorID=12523<br />
|AuthorName=Margaretha<br />
|AuthorFullName=Margaretha Breil}}<br />
<br />
[[Category:Integrated coastal zone management]]</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Effect_of_climate_change_on_coastline_evolution&diff=76279Effect of climate change on coastline evolution2019-12-16T11:28:15Z<p>Dronkers J: </p>
<hr />
<div>Global warming causes sea-level rise as oceans expand, and makes storm patterns more energetic. Consequently it will affect most of the world’s coastlines through inundation and increased erosion. Sound predictions of the development of these hazards over the next century are needed in order to manage the resulting risks. Coastal flooding is somewhat easier to predict than erosion since inundation can be estimated using coastal contours. However its prediction is not trivial since inundation may be followed by rapid reshaping of the shoreline by, amongst other things, waves, tidal currents and human interventions.<br />
<br />
Understanding of coastal morphological response to climate change and sea-level rise is quite underdeveloped. This is partly because the timescales over which concern of its effects are greatest (annual to centennial) falls between the small scales addressed by most numerical models and the large sales described in the conceptual models of geomorphologists. An additional problem is that the type of model often used to bridge this gap, which is based on extrapolation of historic behaviour, is inappropriate if the climate changes. <br />
<br />
__TOC__<br />
<br />
==Coastline response to accelerated sea-level rise==<br />
The most widely cited method of quantifying the response of a shore to rising sea-levels is known as the [[Bruun rule]]. This was developed to describe the behaviour of sandy coasts with no cliff or shore platform. It assumes that the wave climate is steady and consequently the (average equilibrium) [[beach profile]] does not change, but does translate up with the sea-level. This rise in beach surface requires sand, which is assumed to be eroded from the upper beach and deposited on the lower beach. Thus as the profile rises with sea level it also translates landward, causing shoreline retreat. Note that despite the erosion of the upper beach no sand is actually lost; it simply translates a small distance down the profile. The Bruun rule has been the subject of some debate and criticism, but is still generally supported (e.g. Stive, 2004<ref>Stive, M. 2004 How important is global warming for coastal erosion? Climatic change 64, 27-39</ref>) and a recent observational study by Zhang et al. (2004)<ref>Zhang, K., Douglas, B., and Leatherman, S. (2004). Global Warming and Coastal Erosion. Climatic Change 64, 41-58</ref> lends weight to it. They found that the Bruun rule modelled retreat of eastern USA shorelines well, although they recognised that it does not represent long-shore transport, and restricted their study to sites where this could be neglected. <br />
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Another constraint on the range of applicability of the Bruun rule results from its assumptions that the shore profile is entirely beach and loses no sediment. Along most coastlines the beach is a surface deposit that can only be eroded by a limited amount before the land underlying it is exposed and attacked. Here the shore profile is composed of both beach and rock. The rock element of such composite shores complicates its behaviour because it can only erode (not accrete) and it is likely to contain material that is lost as fine sediment. In addition, being purely erosive and relatively hard, it will have a different equilibrium profile to that of the beach and will take longer to achieve it.<br />
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Modifications to the Bruun rule can be used to account for the loss of fine sediment (cfi Bray & Hooke 1997<ref>Bray MJ, Hooke JM (1997) Prediction of coastal cliff erosion with accelerating sea-level rise. J Coast Res 13, 453–467</ref>) but not changes in profile form. Relatively little work has been done on the relationship between sea-level rise and the profiles of composite beach/rock shores. Recent results indicate that such profiles do change, becoming steeper as the rate of sea-level rise increases (Walkden & Hall, 2005<ref>Walkden M.J. and Hall J.W. (2005) A predictive mesoscale model of the erosion and profile development of soft rock shores. Coast Engineering 52, 535–563</ref>).<br />
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The Bruun rule predicts that rates of increase of sea-level rise and shoreline recession will be the same, i.e. R2/R1 = S2/S1 where R and S are the rates of equilibrium recession and sea-level rise respectively and 1 and 2 indicate historic and future conditions. Walkden & Dickson (2006)<ref>Walkden M and Dickson M, (2008) Equilibrium erosion of soft rock shores with a shallow or absent beach under increased sea level rise. Marine Geology, Vol 251/1-2 pp 75-84 DOI: 10.1016/j.margeo.2008.02.003</ref> predicted that low beach volume composite shores are rather less sensitive and that, for them, R2/R1 = sqrt(S2/S1), although, like the Bruun rule, this equation does not account for longshore interactions.<br />
<br />
Dickson at al (2007) <ref>Dickson, M.E., Walkden, M.J., and Hall, J.W., (2007) Systemic impacts of climate change on an eroding coastal region over the twenty-first century. Climatic Change 84(2), PP.141-166. DOI 10.1007/s10584-006-9200-9</ref> modelled alongshore interactions along a 50 km stretch of composite beach/ rock coast under a range of sea-level rise scenarios. They demonstrated a marked increase in complexity of shore response to sea-level rise in areas where alongshore sediment transport was important, even observing some shoreline advance.<br />
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Shore wave heights are normally limited by water depth, so an increase in sea-level might be expected to increase waves at the shore. This appears to be true at composite beach/ rock shores, however it does not necessarily occur at beach shores. Bruun’s model describes beach profiles remaining constant as they translate up and landward. This means that although the sea-level rises the water depth across the surf zone does not increase, and so larger waves can not be accommodated.<br />
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==Coastline response to changed storm patterns==<br />
The form of a shoreline depends strongly on the climate of wave conditions it is exposed to. Larger waves are better able to erode both beach and land. The angle at which waves arrive has a strong effect on the rate at which beach material is redistributed along the shore. A shoreline may therefore represent a dynamic balance between the wave climate, land erosion and the distribution of beach sediment. Changes to the wave climate, such as a shift in average direction or a general increase in height will disturb this balance, and a period of shoreline adjustment would be expected. <br />
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Interaction of neighbouring coasts makes such shoreline adjustment complex and difficult to predict. Fortunately [[Littoral drift and shoreline modelling|One Line morphological models]] are able to represent alongshore beach movement at large spatial and temporal scales. Studies that have used this approach to predict shore response to wave climate change have found differing shoreline sensitivity. Slott et al. (2006)<ref>Slott J.M. Murray, A.B., Ashton, A.D. and Crowley, T.J. (1996) Coastline responses to changing storm patterns. Geophysical Research Letters 33 (18)</ref> found such shoreline change could be an order of magnitude greater than those caused by rising sea levels. Conversely Dickson et al. (2007) found both smaller overall sensitivity and that sea-level rise had a stronger effect. This difference is unsurprising because the two studies examined coasts that are different in many ways; Slott et al. dealt with sandy cuspate shores exposed to high angle waves, whereas Dickson et al. modelled composite beach/ rock shores. It appears that the high dependency of cuspate shores on wave angle strongly increases their sensitivity to changes in wave climate, relative to composite beach/ rock shores.<br />
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==Related articles==<br />
<br />
* [[Sea level rise]]<br />
* [[Bruun rule for shoreface adaptation to sea-level rise]] <br />
* [[Potential Impacts of Sea Level Rise on Mangroves]]<br />
* [[Shoreface profile]]<br />
* [[Climate adaptation policies for the coastal zone]]<br />
* [[Littoral drift and shoreline modelling]]<br />
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==References==<br />
<references/><br />
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{{author<br />
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[[Category:Climate change, impacts and adaptation]]<br />
[[Category:Sea level rise]]</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Talk:Statistical_description_of_wave_parameters&diff=76278Talk:Statistical description of wave parameters2019-12-15T16:29:56Z<p>Dronkers J: Created page with "Job Dronkers (December 2019): I have added two appendices with explanations, definitions and formulas."</p>
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<div>Job Dronkers (December 2019): I have added two appendices with explanations, definitions and formulas.</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Statistical_description_of_wave_parameters&diff=76277Statistical description of wave parameters2019-12-15T16:27:53Z<p>Dronkers J: </p>
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Because of the random nature of natural waves, a statistical description of the waves is normally always used. Observed wave heights often follow the Rayleigh distribution. Statistical wave parameters are calculated based on this distribution. The most commonly used variables in coastal engineering are described below.<br />
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==Most commonly used variables in coastal engineering==<br />
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===Significant wave height===<br />
<br />
[[image:timeseries.jpg|400px|thumb|left|Fig. 1. Time-series of surface elevations by individual waves for a certain sea state.]]<br />
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An example of a wave record representative for a certain sea state is shown in Fig. 1. The significant wave height, <math>H_s</math>, is the mean of the highest third of the waves; instead of <math>H_s</math> the notation <math>H_{1/3}</math> is also often used. <math>H_s</math> corresponds well with the average height of the highest waves in a wave group. The significant wave height can also be computed from the wave energy; it is then referred to as <math>H_{m0}</math>. In practice it appears that <math>H_{m0} \approx H_s</math>. An explanation, definitions and formulas are given in appendix A.<br />
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===Mean wave period===<br />
The mean wave period, <math>T_m</math>, is the mean of all wave periods in a time-series representing a certain sea state.<br />
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===Peak wave period===<br />
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[[image:wavespectrum.jpg|right|thumb|Fig. 2. Wave spectrum: <math>H_{m0}=1m, T_{02}=3.55s, T_p=5s</math> (corresponding to peak frequency of 0.2 <math>s^{-1}</math>)]]<br />
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The peak wave period, <math>T_p</math>, is the wave period with the highest energy. The analysis of the distribution of the wave energy as a function of wave frequency <math>f=1/T</math> for a time-series of individual waves is referred to as a spectral analysis. Wind wave periods (frequencies) often follow the so-called JONSWAP or Pierson-Moskowitz spectra (see appendix B). The peak wave period is extracted from the spectra. As a rule of thumb the following relation can be used: <br />
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<math>T_p \approx 5 \sqrt{H_{m0}}. \qquad (1) </math><br />
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===Mean wave direction===<br />
The mean wave direction, <math>\theta_m</math>, is defined as the mean of all the individual wave directions in a time-series representing a certain sea state.<br />
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==Description of wave conditions==<br />
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These parameters are often calculated from continuous or periodic time-series of the surface elevations; typically the parameters are calculated once every one or three hours, whereby a new discrete time-series of the statistical wave parameters is constructed. This time-series is thereafter analysed statistically to arrive at a condensed description of the wave conditions as follows:<br />
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*Wave height distribution represented by <math>H_s</math> vs. percentage of exceedance. This often follows a Weibull-distribution (see appendix A and the example in Fig. 3);<br />
*Directional distribution of the wave heights, which is often presented in the form of a wave rose (see appendix B and the example in Fig. 4);<br />
*Scatter diagram of <math>T_p</math> vs. <math>H_s</math> (example in Fig. 5).<br />
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{| border="0"<br />
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[[File:WaveHeightExceedanceDistribution.jpg|thumb|300px|left|Fig. 3. Wave height exceedance distribution for various wave directions; wave climate from the West Coast of Denmark. ]]<br />
| valign="top"|<br />
[[File:WaveHeightDirectionalSpreading.jpg|thumb|left|300px||Fig. 4. Wave height directional distribution, a so-called wave rose. Wave climate from the West Coast of Denmark.]]<br />
| valign="top"|<br />
[[File:ScatterDiagramWavePeriodWaveHeight.jpg|thumb|left|300px|Fig. 5. Scatter diagram of <math>T_p</math> vs. <math>H_{m0}</math>; wave climate from the West Coast of Denmark. The approximate empirical relation between <math>T_p</math> and <math>H_{m0}</math> for storm waves is also shown. ]]<br />
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Analyses of extreme wave conditions are performed on the basis of max. wave heights in single storm events or on the basis of annual max. wave heights. These analyses are often presented as exceedence probability vs. wave heights, see Fig. 6 for an example.<br />
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[[image:extreme value.jpg|thumb|center|500px|Fig. 6. Extreme value analysis of wave height by Weibull distribution. Threshold = 2 m.]]<br />
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==Further reading==<br />
* Mangor, K., Drønen, N.K., Kaergaard, K.H. and Kristensen, S.E. 2017. Shoreline Management Guidelines. DHI Water and Environment, 451pp. <ref>https://www.dhigroup.com/upload/campaigns/ShorelineManagementGuidelines_Feb2017.pdf</ref><br />
* Coastal Engineering Manual, part II, chapter 1. US Army Corps of Engineers (USACE), 2008<br />
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==Appendix A: Rayleigh distribution==<br />
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The wave contribution to the ocean sea level <math>\eta(x,y,t)</math> at a certain location <math>x,y</math> is generally a superposition of a large number <math>n</math> of random waves with amplitudes <math>a_j</math>, radial frequencies <math>\omega_j</math> and random phases <math>\phi_j</math>, originating from different nearby and remote regions. This superposition can be represented by <br />
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<math>\eta=Re[\sum_{j=1}^{n} a_j \exp(i\omega_j t + i\phi_j)]. \qquad (A1)</math><br />
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The statistical distribution of wave heights was derived by Longuet-Higgins (1952)<ref>Longuet-Higgins, M.S. 1952. On the statistical distribution of sea waves. Journal of Marine Research 11: 245-266</ref> under a few specific conditions: (a) the random numbers <math>a=\sum_{j=1}^{n} a_j \cos\phi_j, \, b=\sum_{j=1}^{n} a_j \sin\phi_j</math> are statistically independent and normally (Gaussian) distributed; (b) the radial frequencies <math>\omega_j</math> of the random waves are grouped in a single narrow band around a central frequency <math>\omega</math> such that <math>|\omega_j -\omega_j'|/ \omega << 1</math> for each <math>j, j'</math>. Under this last condition the expression (A1) may be approximated for the time interval [<math>-\pi / \omega <t< \pi / \omega</math>] by<br />
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<math>\eta \approx Re[ \exp(i \omega t) \sum_{j=1}^{n} a_j \exp(i\phi_j)] \equiv \frac{1}{2} H \, Re[\exp(i \omega t+i \phi)] , \quad H = 2 \sqrt{a^2 + b^2} . \qquad (A2)</math> <br />
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A well-known mathematical theorem<ref>https://en.wikipedia.org/wiki/Rayleigh_distribution</ref> states that the length of a vector with Gaussian distributed components follows the Rayleigh distribution. In this case the vector length is the wave height <math>H</math> and the components are the random numbers <math>2a, 2b</math>. The Rayleigh probability density function <math>p_R(H)</math> for the wave height <math>H</math> reads:<br />
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<math>p_R(H) = \Large\frac{2H}{H_{rms}^2}\normalsize \exp\Large (–(\frac{H}{H_{rms}})^2)\normalsize . \qquad (A3)</math><br />
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The mean square root wave heigth <math>H_{rms}</math> is related to the average wave energy <math>\overline E</math>:<br />
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<math> H_{rms}^2 = \int_0^{\infty} p_R(H) H^2 dH =\Large\frac{8}{g \rho}\normalsize \overline E. \qquad (A4)</math> <br />
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The average wave height <math>\overline H</math> is related to the mean square root wave height <math>H_{rms}</math> by<br />
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<math>\overline H= \int_0^{\infty} p_R(H) H dH = \Large\frac{\sqrt{\pi}}{2}\normalsize H_{rms} <br />
\approx 0.89 H_{rms} .\qquad (A5)</math> <br />
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The cumulative Rayleigh distribution (probability of wave height <math><H</math>) is given by<br />
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<math>P_R(H)=\int_0^H p_R(H')dH' = 1-\exp\Large (-(\frac{H}{H_{rms}})^2)\normalsize .\qquad (A6) </math><br />
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For calculating <math>H_{1/3}</math> (the mean of the highest third of the waves) we first determine the lowest of the largest third waves, <math>H_l</math>, from the condition <math>P_R(H_l)=2/3</math>, yielding <math>H_l=H_{rms} \ln(3)</math>. The significant wave height <math>H_s \equiv H_{1/3}</math> is given by<br />
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<math>H_s=\Large\frac{\int_{H_l}^{\infty} p_R(H)HdH}{\int_{H_l}^{\infty} p_R(H)dH }\normalsize \approx 1.6 \overline H = 1.42 H_{rms}. \qquad (A7)</math><br />
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From (A4), (A5) and (A7) it follows that <math>H_s</math> is related to the average wave energy <math>\overline E</math>:<br />
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<math>H_s \approx H_{m0} \equiv 4 \Large \sqrt{ \frac{\overline E}{g \rho}}\normalsize . \qquad(A8)</math><br />
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Extreme wave heights can be derived from the Rayleigh distribution in a similar way. For example, the mean of the 1% highest waves is given by<br />
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<math>H_{1/100} \approx 2.36 H_{rms} . \qquad (A9)</math><br />
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In spite of the restrictive conditions for which the Rayleigh distribution has been derived, it appears that in many cases it corresponds reasonably well with wave height statistics obtained from field observations, even if the conditions (a) and (b) are not well satisfied.<br />
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However, the Rayleigh distribution does not put a limit on the wave height, which is physically unrealistic and leads to overestimation of the highest waves. Therefore often the Weibull distribution is used instead of the Rayleigh distribution. The Weibull distribution <ref>https://en.wikipedia.org/wiki/Weibull_distribution</ref> reads:<br />
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<math>p_W(H)=\Large\frac{m}{\lambda}(\frac{H}{\lambda})^{(m-1)}\normalsize \exp\Large (–(\frac{H}{\lambda})^{m}) \normalsize . \qquad (A10)</math><br />
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The Rayleigh distribution corresponds to the Weibull distribution for <math>m=2, \; \lambda=H_{rms}</math>. The Weibull distribution has an additional parameter (<math>m</math>) that allows suppression of the highest waves for <math>m>2</math> and an optimum adjustment to the observed wave data.<br />
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This is especially relevant for shallow-water waves, which are truncated due to depth-induced wave breaking. For this situation, alternative distributions have been proposed, for example by Battjes and Groenendijk (2000)<ref> Battjes, J.A. and Groenendijk, H.W. 2000. Wave height distributions on shallow foreshores. Coastal Engineering 40: 161-182</ref>. According to this study, a Weibull distribution with <math>m=3.6</math> should be used above a certain threshold, <math>H_{tr}</math>. <br />
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==Appendix B: Frequency spectrum==<br />
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A wave record can further be characterized by its frequency spectrum. The energy density spectrum of a sea state is generally designated by <math>E(f)</math>. The total energy is given by<br />
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<math>\overline E=\int_0^{\infty} E(f)df . \qquad (B1)</math><br />
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The wave frequency spectrum can be determined from a wave record by using a Fourier transform. It can also be determined by modelling the wind-induced wave field in a large source area. Empirical formulas have been established for fully developed wave fields under constant wind stress. For deep water without fetch restriction, it is recommended to use the adapted Pierson-Moskowitz frequency distribution <math>E_{PM}</math> <ref>The Rock Manual. The use of rock in hydraulic engineering (2nd edition).CIRIA. London, 2007</ref>:<br />
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<math>E_{PM}(f)=3.26 \Large\frac{\overline E}{f_p}(\frac{f_p}{f})^4 e^{-(\frac{f_p}{f})^4}\normalsize . \qquad (B2)</math><br />
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For the average wave energy <math>\overline E</math> and the peak frequency <math>f_p</math> the following empirical expressions are found:<br />
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<math>\overline E \approx 0.005 \rho g^{-1} U_{10}^4\; , \; f_p \approx 0.123 g U_{10}^{-1} \;,</math> <br />
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where <math>g</math> is the gravitational acceleration and <math>U_{10}</math> the wind velocity at 10 m above the sea surface.<br />
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For fetch-limited seas, the spectrum is more strongly peaked around the peak frequency. For this situation, the empirical JONSWAP spectrum can be used. It has the form<br />
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<math>E_{WONSJAP}=\Large\frac{\alpha \rho g^3}{f_p (2 \pi f_p)^4} (\frac{f_p}{f})^4 e^{-(\frac{f_p}{f})^4}\normalsize \gamma^\delta \;, \quad \delta =e^{-\Large\frac{1}{2}\Large(\frac{(f/f_p)-1}{\sigma})^2}\normalsize , \qquad (B3)</math>,<br />
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where the parameters <math>\alpha, \gamma, \sigma, f_p</math> depend on the fetch length and should be fitted to the wave data. For <math>\gamma=1</math> the Pierson-Moskowitz and JONSWAP spectra are the same.<br />
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Different characteristic wave periods can be derived from the wave spectrum: the significant wave period <math>T_{01}</math>, the mean wave period <math>T_{02}</math> and the mean energy period <math>T_E</math>. They are given by the expressions<br />
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<math>T_{01}=\Large\frac{\int_0^{\infty} E(f)df}{\int_0^{\infty} E(f)fdf }\normalsize, \quad T_{02}=\Large \sqrt{\frac{\int_0^{\infty} E(f)df}{\int_0^{\infty} E(f) f^2 df }}\normalsize, \quad T_E=\Large\frac{\int_0^{\infty} E(f) f^{-1} df}{\int_0^{\infty} E(f)df }\normalsize \; .\qquad (B4) </math><br />
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For the Pierson-Moskowitz distribution (B2) we have<br />
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<math>T_{01}=0.69 \, T_p, \; T_{02}=0.58 \, T_p, \; T_E=0.82 \, T_p </math>.<br />
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A closer estimate of the peak period <math>T_p=1/f_p</math> can be obtained by using a higher power of the energy density spectrum, for example<br />
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<math>\Large\frac{\int_0^{\infty} E^5(f)df}{\int_0^{\infty} E^5(f)fdf }\normalsize \approx 0.95 T_p</math>.<br />
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In the fetch-limited case with a JONSWAP-type spectrum the value of <math>T_E</math> is generally found close to the peak period <math>T_p</math>. <br />
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In an irregular wave field, waves may come from different directions. The wave incidence direction is an important parameter for sediment transport in the coastal zone. Waves originating from different areas may have different spectra. The directional spread of incoming waves for a particular wave frequency can be represented by a distribution function <math>D(f,\theta)</math>, where <math>\theta</math> is the wave incidence angle. We then have<br />
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<math>\overline E \equiv \int_0^{\infty} \int_0^{2 \pi} S(f, \theta) df d \theta \equiv \int_0^{\infty} \int_0^{2 \pi} E(f) \, D(f, \theta) df d \theta \; ,\quad \int_0^{2 \pi} D(f, \theta) d \theta =1 \; .\qquad (B5) </math><br />
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The directional wave spectrum <math>S(f, \theta)</math> can be derived from directional wave buoys. In practice, it is often obtained by numerical modelling of the wave field in the major source area.<br />
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==References==<br />
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{{author<br />
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[[Category:Physical coastal and marine processes]]<br />
[[Category:Hydrodynamics]]</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=File:WaveHeightDirectionalSpreading.jpg&diff=76276File:WaveHeightDirectionalSpreading.jpg2019-12-14T16:58:38Z<p>Dronkers J: Wave height directional distribution, a so-called wave rose.</p>
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<div>== Summary ==<br />
Wave height directional distribution, a so-called wave rose.</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=File:ScatterDiagramWavePeriodWaveHeight.jpg&diff=76275File:ScatterDiagramWavePeriodWaveHeight.jpg2019-12-14T16:57:53Z<p>Dronkers J: Scatter diagram of <math>T_p</math> vs. <math>H_{m0}</math>.</p>
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<div>== Summary ==<br />
Scatter diagram of <math>T_p</math> vs. <math>H_{m0}</math>.</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=File:WaveHeightExceedanceDistribution.jpg&diff=76274File:WaveHeightExceedanceDistribution.jpg2019-12-14T16:56:55Z<p>Dronkers J: Wave height exceedance distribution for various wave directions.</p>
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<div>== Summary ==<br />
Wave height exceedance distribution for various wave directions.</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Continental_Nutrient_Sources_and_Nutrient_Transformation&diff=76213Continental Nutrient Sources and Nutrient Transformation2019-12-04T21:15:07Z<p>Dronkers J: </p>
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Nutrients in coastal environments come from various sources - through rivers, groundwater or atmospheric deposition. The main species - Nitrogen, Phosphorus and Silicon - undergo different transformation processes and states. <br />
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==Continental nutrient sources==<br />
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===Rivers===<br />
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On a global scale, riverine inputs of N and P to coastal seas have possibly increased by factors of 2 to 3 in the period 1960-1990<ref name=”Howarth”>Howarth, R., H. Jensen, R. Marino, and H. Postma, in Phosphorus in the Global Environment:Transfers, Cycles and Management, H. Tiessen, Ed., Scientific Committee on Problems of the Environment 54. (Wiley, New York, 1995), pp. 323–356.</ref> <ref name=”Duce”> Duce, R., P.S. Liss, J.T. Merrill, E.L. Atlas, P. Buat-Menard, B.B. Hicks, J.M. Miller, J.M. Prospero, R. Arimoto, T.M. Church,. W. Ellis, J.N. Galloway, L. Hansen, T.D. Jickells, A.H. Knap, K.H. Reinhardt, B. Schneider, A. Soudine, J.J. Tokos, S. Tsunogai, R. Wollast, and M. Zhou (1991), The atmospheric input of trace species to the world ocean, Global Biogeochemical Cycles 5, 193-296.</ref> <ref name="Jickells 1998">Jickells T.D. (1998), Nutrient Biogeochemistry of the Coastal Zone, Science, 281 217 – 222</ref>. Agriculture, in the form of fertilizers, leachates and animal wastes, is the largest contributor of N and P in aquatic systems <ref name=”Howarth”>Howarth, R., H. Jensen, R. Marino, and H. Postma, in Phosphorus in the Global Environment:Transfers, Cycles and Management, H. Tiessen, Ed., Scientific Committee on Problems of the Environment 54. (Wiley, New York, 1995), pp. 323–356.</ref> . Other major inputs include point-source discharges of wastewater from urban sewer networks<ref name=”B&G2007”> Billen, G., J. Garnier, J. Nemery, M. Sebilo, A. Sferratore, S. Barles, P. Benoit, and M. Benoit (2007), A long-term view of nutrient transfers through the Seine river continuum, Science of the Total Environment 375, 80-97.</ref> <ref name=”EEA1999”> European Environment Agency (1999), Nutrients in European Ecosystems. Environmental Assessment Report No. 4, Office for Official Publications of the European Communities, Luxembourg, pp. 156.</ref> and industrial wastes. The direct discharge of P exchanged with soils and sediments <ref name=”B1991”> Billen, G., C. Lancelot, and M. Meybeck (1991), N, P and Si retention along the aquatic continuum from land to ocean. Ocean Margin Processes in Global Change, R.F.C Mantoura, J.-M. Martin, and R. Wollast, Eds. (John Wiley & Sons Ltd.), pp. 19-44.</ref> also contributes significantly to the budget of this element. <br />
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Riverine Si fluxes, originating predominantly from weathering, have generally been altered little by human activity<ref name="Jickells 1998"/> . <br />
<br />
However, human management of rivers has, in some cases, altered the Si fluxes extensively<ref name=”Humborg2002”> Humborg, C, S. Blomqvist, E. Avsan, Y. Bergensund, E. Smedberg, J. Brink, and C.-M. Morth (2002), Hydrological alterations with river damming in northern Sweden: implications for weathering and river biogeochemistry, Global Biogeochemical Cycles, 16 (3), 1039</ref> , often leading to a reduction in diatom blooms as a result of damming.<br />
<br />
===Groundwater===<br />
<br />
The direct discharge of groundwater into the ocean, termed submarine groundwater discharge (SGD), has been recently recognized as an additional pathway of nutrients from the land to coastal waters <ref name="Johannes1980">Johannes, R.E. (1980), The ecological significance of the submarine discharge of groundwater, Marine Ecology-Progress Series 3, 365-373.</ref> <ref name=”Capone1985”> Capone, D.G., and M.F. Bautista (1985), A groundwater source of nitrate in nearshore marine sediments, Nature 313, 214 216.</ref>, see the article [[Submarine groundwater discharge and its influence on the coastal environment]]. On a global scale, SGD rates vary between 0.01-10 % of river runoff<ref name=”Church1996”>Church, T.H. (1996), An underground route for the water cycle, Nature 380, 579-580.</ref>. However, the concentrations of nutrients in groundwater are typically higher than those in coastal and river waters <ref name="Johannes1980"/> <ref name="Valiela1990">Valiela, I., J. Costa, K. Foreman, J. Teal, B. Howes, and D. Aubrey (1990), Groundwater-borne inputs from watersheds to coastal waters, Biogeochemistry 10, 177-198.</ref> <ref name="Dollar1992">Dollar, S.J., and M.J. Atkinson (1992), Effects of nutrient subsidies from groundwater to nearshore marine ecosystems off the island of Hawaii, Estuarine, Coastal and Shelf Science 35, 409-424.</ref> <ref name="Moore1996">Moore, W.S. (1996), Large groundwater inputs to coastal waters revealed by 226Ra enrichments, Nature 380, 612-614.</ref> <ref name=”Uchiyama2000”>Uchiyama, Y., K. Nadaoka, P. Rolke, K. Adachi, and H. Yagi (2000), Submarine groundwater discharge into the sea and associated nutrient transport in a sandy beach, Water Resources Research 36, 1467-1479.</ref>. Therefore, in terms of fluxes, such high concentrations can compensate for the relatively low SGD rates. At the local scale, SGD of nutrients is a prominent transport pathway, particularly in enclosed bays, karstic and fractured systems (e.g., Hawaii<ref name="Garison2003">Garrison, G.H., C.R. Glenn, and G.M. McMurty (2003), Measurement of submarine groundwater discharge in Kahana Bay, O’ahu, Hawaii, Limnology and Oceanography 48, 920-928.</ref>), or at locations where rivers are small or non-existent (e.g., Yucatan peninsula<ref name="Hanshaw1980"> Hanshaw, B.B., and W. Back (1980), Chemical mass-wasting of the northern Yucatan Peninsula by groundwater dissolution, Geology 8, 222-224.</ref>).<br />
<br />
===Atmosphere===<br />
<br />
Atmospheric deposition is a significant source of N compounds to the coastal zone, particularly in summer and autumn, but is only a minor source of Si and P<ref name="Conley1993">Conley D.J., C.L. Schelske, and E.F. Stoermer (1993), Modification of the biogeochemical cycle of silica with eutrophication, Marine Ecology-Progress Series 101, 179–192.</ref> <ref name=”Conley2000”>Conley D.J., P. Stalnacke, H. Pitkanen, and A. Wilander (2000), The transport and retention of dissolved silicate by rivers in Sweden and Finland, Limnology and Oceanography 45, 1850–1853.</ref>,<ref name="Jickells 1998"/>. Nitrogen delivered by the atmospheric pathway can be either in the oxidized or reduced form<ref name=”Galloway1995”> Galloway J., W. Chlesinger, H. Levy, A. Michaels, and J. Schnoor (1995), Nitrogen fixaton: Anthropogenic enhancement and environmental response, Global Biogeochemical Cycles 9, 235-252.</ref> . For instance, atmospheric deposition amounts to 30% of the total land based nitrogen input to the North Sea, mainly as oxidized N, and 50% to the Baltic Sea<ref name=”NorthSeaTaskForce1993”> North Sea Task Force (1993), North Sea Quality Status Report, Oslo and Paris Commissions, London. Olsen & Olsen, Fredensborg, Denmark.</ref> . The N:Si:P ratio for wet deposition in the North Sea is 503:2:1<ref name=”Rendell1993”> Rendell, A. R., Ottley, C. J., Jickells, T. D. & Harrison, R. M. Tellus 45, 53−63 (1993).</ref> .<br />
<br />
==Nutrient transformation==<br />
Nutrients are significantly altered by biogeochemical processes during their transport along the land-ocean transition zone, especially in [[Estuaries|estuarine]] systems. Figure 1 summarizes the major N sources and transformation processes in an estuary. Estuaries are usually turbid, and hence primary production is often limited by light availability. Light conditions generally improve towards the [[coastal zone]] and [[primary production]] becomes a dominant process in controlling the biogeochemical cycles of nutrients<ref name="Jickells 1998"/>. <br />
<br />
[[Image:Uses3.jpg|thumb|right| Fig.1. Bioturbated seabed.]]<br />
Sediments cover most of the seabed and hence most of the earth. [[Recycling of carbon and nutrients]] within this habitat (both subtidally and intertidally) is critical both at small and large scales. The availability of essential nutrients, such as nitrogen and phosphorus, and metals is essential for life. Processes that aid nutrient cycling are crucial to ecosystem functioning, as this increases the availability of nutrients and thus maintains productivity of the system. For example, in the marine benthic environment, bioturbation by marine worms, mainly through burrowing in the sediment, moves nutrients from deep sediment layers to the surface and vice versa (Fig. 1). Nutrient cycling is also maintained through processes such as ingestion and excretion of materials by organisms e.g. fish mineralise nitrogen and phosphorus through excretion. <br />
<br />
<br />
===Nitrogen===<br />
N species in aquatic environments include dissolved (nitrate, nitrite, ammonium, organic N) and particulate (organic N) constituents<ref name="Tappin 2002"> Tappin, A.D. (2002), An Examination of the Fluxes of Nitrogen and Phosphorus in Temperate and Tropical Estuaries: Current Estimates and Uncertainties, Estuarine, Coastal and Shelf Science 55, 885-901. </ref> . The removal of N occurs by deposition and permanent burial in sediments and, most importantly, loss to the atmosphere by bacterial [[denitrification]]. This process is coupled with organic matter decomposition and reduces nitrate to gaseous N<sub>2</sub>/N<sub>2</sub>O under anoxic conditions. Part of the nitrate pool originates from coupled nitrification/denitrification, in which the ammonium produced from organic matter degradation is first oxidized to nitrate, and subsequently denitrified <ref name="Jickells 1998"/>. In temperate and tropical estuaries the estimated loss of nitrate N via denitrification varies widely, and also varies in time and space within estuaries<ref name=”Barnes1998”> Barnes, J., and N.J.P. Owens (1998), Denitrification and nitrous oxide concentrations in the Humber Estuary, UK, and adjacent coastal zones, Marine Pollution Bulletin 37, 247–26.</ref> <ref name=”Dong2000”> Dong, L.F., D.C.O. Thornton, D.B. Nedwell, and G.J.C. Underwood (2000), Denitrification in sediments of the River Colne estuary, England, Marine Ecology Progress Series 203, 109–122.</ref> . Because denitrification requires low oxygen concentrations, this process is particularly important in muddy sediments<ref name=”Seitzinger1998”> Seitzinger, S.P. 1988. Denitrification in freshwater and coastal marine ecosystems: ecological and geochemical importance. Limnology and Oceanography 33:702-724.</ref> <ref name=”Malcolm1997”> Malcolm, S.J. and Sivyer, D.B., 1997. Nutrient recycling in intertidal sediments. in Jickells, T. and Rae, J.E. (Eds) Biogeochemistry of Intertidal Sediments. Cambridge University Press, pp. 59–83.</ref> . It is also quantitatively more important in ecosystems characterized by relatively long residence times<ref name=”Nixon1995”> Nixon, S.W. (1995), Coastal marine eutrophication: A definition, social causes, and future concerns, Ophelia 41, 199–219.</ref> . In groundwater systems, the nitrate supplied either by infiltrating water or produced through nitrification<ref name=”Horrigan1985”> Horrigan, S.G., and Capone, D.G (1985), Rates of nitrification and nitrate reduction in nearshore marine sediments under varying environmental conditons, Marine Chemistry 16, 317-327</ref> <ref name=”Nowicki1999”> Nowicki, B.L., E. Requintina, D. van Keuren, and J. Portnoy (1999), The role of sediment denitrification in reducing groundwater-derived nitrate inputs to Nauset Marsh Estuary, Cape Cod, Massachusetts, Estuaries 22, 245-259.</ref> is also commonly removed through denitrification. As in surface estuaries, a set of conditions, namely the presence of labile organic matter, a low redox potential and sufficient time for reaction, are prerequisite for effective denitrification to occur. However, field studies often report only limited nitrate removal prior to discharge to coastal waters primarily due to a lack of labile dissolved organic matter<ref name=”Star1993”> Starr, R.C., and R.W. Gillham (1993), Denitrification and organic-carbon availability in two aquifers, Ground Water 31, 934–947.</ref> <ref name=”Slater1987”> Slater, J.M., and D.G. Capone (1987), Denitrification in aquifer soil and nearshore marine sediments influenced by groundwater nitrate, Applied and Environmental Microbiology 53, 1292-1297.</ref> <ref name=”DeSimone1996”> DeSimone, L.A., and B.L. Howes (1996), Denitrification and nitrogen transport in a coastal aquifer receiving wastewater discharge, Environmental Science and Technology 30, 1152-1162.</ref>, as is the case in many shallow groundwater aquifers or sandy nearshore sediments, or due to high groundwater velocities<ref name="Capone1990">Capone, D.G., and J.M. Slater (1990), Interannual patterns of water-table height and groundwater derived nitrate in nearshore sediments, Biogeochemistry 10, 277-288.</ref> <ref name=”Giblin1990”> Giblin, A.E., and A.G. Gaines (1990), Nitrogen inputs to a marine embayment: The importance of groundwater, Biogeochemistry 10, 309-328.</ref> .<br />
<br />
===Phosphorus===<br />
<br />
P species in aquatic systems include dissolved (inorganic, organic P) and particulate (inorganic, organic P) constituents<ref name="Tappin 2002"/> . The retention of P in the land-ocean transition zone is often attributed to adsorption on solid particles, which are constantly trapped in estuarine sediments<ref name=”Jickells1991”> Jickells, T.D., T.H. Blackburn, J.O. Blanton, D. Eisma, S.W. Fowler, R.F.C. Manroura, C.S. Martens, A. Moll, R. Scharek, K.I. Suzu, and D. Vaulot (1991), What determines the fate of material within ocean margins? Ocean Margin Processes in Global Change, R.F.C Mantoura, J.-M. Martin, and R. Wollast, Eds. (John Wiley & Sons Ltd.), pp. 211–234.</ref> , or forms part of the solid matrix in coastal aquifers. However, in the case of very large rivers that discharge directly in the continental shelf, P retention in the mixing zones between freshwater and seawater will be limited <ref name=”Milliman1991”> Milliman, J.D. (1991), in Ocean Margin Processes in Global Change, R.F.C Mantoura, J.-M. Martin, and R. Wollast, Eds. (John Wiley & Sons Ltd.), pp. 69–90.</ref> . Adsorption onto solids such as iron and aluminum oxides is particularly effective<ref name=”Krom1980”> Krom, M.D., and R.A. Berner (1980), Adsorption of phosphate in anoxic marine sediments, Limnology and Oceanography 25, 797-806.</ref> <ref name=”Frossard1995”> Frossard, E., M. Brossard, M.J. Hedley, and A. Metherell (1995), Reactions controlling the cycling of P in soils. Phosphorus in the global environment, H. Tiessen, Ed. (John Wiley & Sons Ltd.), pp. 107-138.</ref> , and thus may be also coupled to the redox conditions <ref name=”Spiteri2007”> Spiteri, C., C.P. Slomp, K. Tuncay, and C. Meile (2007), Modeling biogeochemical processes in subterranean estuaries: The effect of flow dynamics and redox conditions on submarine groundwater discharge, Water Resources Research, doi:10.1029/2007WR006071.</ref> . For instance, removal of P is very efficient in subterranean estuaries characterized by zones of iron oxide accumulation, (“Iron Curtains” <ref name=”Charette2002”> Charette, M.A., and E.R. Sholkovitz (2002), Oxidative precipitation of groundwater-derived ferrous iron in the subterranean estuary of a coastal bay, Geophysical Resources Letters 29, art. no.-1444.</ref> <ref name=”Spiteri2006”> Spiteri, C., P. Regnier, C.P. Slomp, and M.A. Charette (2006), pH-Dependent iron oxide precipitation in a subterranean estuary, Journal of Geochemical Exploration 88, 399-403.</ref> ). The behavior of P in estuarine systems is also influenced by the strong physico-chemical gradients, which result from the variations in pH, ionic strength and solution composition between the freshwater and seawater end-members (e.g. <ref name=”Froelich1998”> Froelich, P.N. (1988), Kinetic control f dissolved phosphate in natural rivers and estuaries: A primer o the phosphate buffer mechanism, Limnology and Oceanography 33, 649-668.</ref> <ref name=”Lebo1991”> Lebo, M.E. (1991), Particle-bound phosphorus along an urbanized coastal plain estuary, Marine Chemistry 34, 225-246.</ref> <ref name=”VadderZee2007”> Van der Zee, C., N. Roevros, and L. Chou (2007), Phosphorus speciation, transformation and retention in the Scheldt estuary (Belgium/The Netherlands) from the freshwater tidal limits to the North Sea, Marine Chemistry doi:10.1016/j.marchem.2007.01.003.</ref> ). The removal of P can occur through bacterial reduction of phosphate to gaseous phosphine. However, little is known on the rate of phosphate-phosphine transformation and its contribution to overall P cycling<ref name=”Gassman1994”> Gassman, G. (1994) Phosphine in the fluvial and marine hydrosphere, Marine Chemistry 45, 197–205.</ref> <ref name="Tappin 2002"/> . <br />
<br />
<br />
Tidal and marginal sediments are considered important sinks of N and P, although a quantitative estimation of their role remains uncertain<ref name=”Carpenter1997”> Carpenter, K. (1997) A critical appraisal of the methodology used in studies of material flux between [[saltmarsh]]es and coastal waters. Biogeochemistry of Intertidal Sediments, T.D. Jickells, and J.E. Rae, Eds. (Cambridge University Press), pp. 59–83.</ref> <ref name=”Ruddy1998a”> Ruddy, G., C. M. Turley, and T.E.R. Jones (1998a), Ecological interaction and sediment transport on an intertidal mudflat I. Evidence for a biologically mediated sediment-water interface. Sedimentary Processes in the Intertidal Zone, K.S. Black, D.M. Paterson, and A. Cramp, Eds. Geological Society of London Special Publications 139, pp. 135–148.</ref> <ref name=”Ruddy1998b”> Ruddy, G., C.M. Turley, and T.E.R. Jones (1998b), Ecological interaction and sediment transport on an intertidal mudflat II. An experimental dynamic model of the sediment-water interface. Sedimentary Processes in the Intertidal Zone. K.S. Black, D.M. Paterson, and A. Cramp, Eds. Geological Society of London Special Publications 139, pp. 149–166.</ref> . On the global scale, it is generally accepted that intertidal sediments are more efficient for P burial than for N<ref name=”Billen1991”> Billen, G., C. Lancelot, and M. Meybeck (1991), N, P and Si retention along the aquatic continuum from land to ocean. Ocean Margin Processes in Global Change, R.F.C Mantoura, J.-M. Martin, and R. Wollast, Eds. (John Wiley & Sons Ltd.), pp. 19-44.</ref> <ref name=”Howarth1995”> Howarth, R., H. Jensen, R. Marino, and H. Postma, Phosphorus in the Global Environment:Transfers, Cycles and Management, H. Tiessen, Ed., Scientific Committee on Problems of the Environment 54. (Wiley, New York, 1995), pp. 323–356.</ref> .<br />
<br />
===Silicon===<br />
<br />
Relevant Si species in the aquatic environments include dissolved Si (DSi), mainly as undissociated monomeric silicic acid, Si(OH)<sub>4</sub>, and particulate Si (biogenic silica, BSiO<sub>2</sub>), which includes the amorphous silica in both living biomass and biogenic detritus in surface waters, soils and sediments. The main transformation processes are the uptake of DSi and the biomineralisation as BSiO2 in plants and organisms, as well as the dissolution of BSiO2 back to DSi. Over sufficiently long time scales, BSiO<sub>2</sub> may undergo significant chemical and mineralogical changes<ref name=”VanCappellan2002”> Van Cappellen, P., S. Dixit, and J. van Beusekom (2002), Biogenic silica dissolution in the oceans: Reconciling experimental and field-based dissolution rates, Global Biogeochemical Cycles 16, 1075, doi:10.1029/2001GB001431.</ref> , even including a complete diagenetic transformation of the opaline silica into alumino-silicate minerals <ref name=”Michalopoulos2000”> Michalopoulos, P., R.C. Aller, and R.J. Reeder (2000), Conversion of diatoms to clays during early diagenesis in tropical, continental shelf muds, Geology 28, 1095-1098.</ref>.<br />
<br />
The major producers of BSiO<sub>2</sub> in marine environments are diatoms. However, other organisms such as [https://en.wikipedia.org/wiki/Radiolaria radiolarians], sponges and [https://en.wikipedia.org/wiki/Golden_algae chrysophytes] may be important local sources of BSiO<sub>2</sub><ref name=”Simpson1981”> Simpspon, T.L. and B.E. Volcani (1981), Silicon and Siliceous Structures in Biological Systems, Springer-Verlag NY, 587 pp </ref> . Large quantities of DSi are also fixed on land by higher plants, forming amorphous silica deposits, known as [https://en.wikipedia.org/wiki/Phytolith phytoliths]<ref name=”Piperno1998”> Piperno, D.L. (1998), Phytolith analysis. An archaeological and geological perspective. London: Academic Press.</ref> . Their role in the Si cycle has only recently been studied<ref name=”Bartoli1983”> Bartoli, F. (1983), The biogeochemical cycle of silicon in two temperate forest ecosystems, Ecological Bulletins (Stockholm) 35, 469–476.</ref> <ref name=”Meunier1999”> Meunier, J.D., F. Colin, and C. Alarcon (1999), Biogenic silica storage in soils, Geology 27, 835-838. </ref> . In general, riverine Si fluxes have been much less altered by human activity than those of N and P. However, increased damming of major rivers has promoted siliceous phytoplankton blooms<ref name=”Billen1991”> Billen, G., C. Lancelot, and M. Meybeck (1991), N, P and Si retention along the aquatic continuum from land to ocean </ref> <ref name="Humborg1997"> Humborg, C., V. Ittekot, A. Cociosu, and B. v. Bdungen (1997), Effect of Danube River dam on Black Sea biogeochemistry and ecosystem structure, Nature 386, 385 – 388.</ref> , and therefore, reduced Si fluxes to the coastal zone. For example, the damming of the Danube has reduced the DSi concentration by more than 50%<ref name="Humborg1997"/>.<br />
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==See also==<br />
Articles in the [[:Category:Eutrophication]].<br />
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==References==<br />
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[[Category:Coastal and marine ecosystems]] <br />
[[Category:Coastal and marine pollution]]<br />
[[Category:Eutrophication]]</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Continental_Nutrient_Sources_and_Nutrient_Transformation&diff=76212Continental Nutrient Sources and Nutrient Transformation2019-12-04T20:58:49Z<p>Dronkers J: </p>
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Nutrients in coastal environments come from various sources - through rivers, groundwater or atmospheric deposition. The main species - Nitrogen, Phosphorus and Silicon - undergo different transformation processes and states. <br />
<br />
==Continental nutrient sources==<br />
<br />
===Rivers===<br />
<br />
On a global scale, riverine inputs of N and P to coastal seas have possibly increased by factors of 2 to 3 in the period 1960-1990<ref name=”Howarth”>Howarth, R., H. Jensen, R. Marino, and H. Postma, in Phosphorus in the Global Environment:Transfers, Cycles and Management, H. Tiessen, Ed., Scientific Committee on Problems of the Environment 54. (Wiley, New York, 1995), pp. 323–356.</ref> <ref name=”Duce”> Duce, R., P.S. Liss, J.T. Merrill, E.L. Atlas, P. Buat-Menard, B.B. Hicks, J.M. Miller, J.M. Prospero, R. Arimoto, T.M. Church,. W. Ellis, J.N. Galloway, L. Hansen, T.D. Jickells, A.H. Knap, K.H. Reinhardt, B. Schneider, A. Soudine, J.J. Tokos, S. Tsunogai, R. Wollast, and M. Zhou (1991), The atmospheric input of trace species to the world ocean, Global Biogeochemical Cycles 5, 193-296.</ref> <ref name="Jickells 1998">Jickells T.D. (1998), Nutrient Biogeochemistry of the Coastal Zone, Science, 281 217 – 222</ref>. Agriculture, in the form of fertilizers, leachates and animal wastes, is the largest contributor of N and P in aquatic systems <ref name=”Howarth”>Howarth, R., H. Jensen, R. Marino, and H. Postma, in Phosphorus in the Global Environment:Transfers, Cycles and Management, H. Tiessen, Ed., Scientific Committee on Problems of the Environment 54. (Wiley, New York, 1995), pp. 323–356.</ref> . Other major inputs include point-source discharges of wastewater from urban sewer networks<ref name=”B&G2007”> Billen, G., J. Garnier, J. Nemery, M. Sebilo, A. Sferratore, S. Barles, P. Benoit, and M. Benoit (2007), A long-term view of nutrient transfers through the Seine river continuum, Science of the Total Environment 375, 80-97.</ref> <ref name=”EEA1999”> European Environment Agency (1999), Nutrients in European Ecosystems. Environmental Assessment Report No. 4, Office for Official Publications of the European Communities, Luxembourg, pp. 156.</ref> and industrial wastes. The direct discharge of P exchanged with soils and sediments <ref name=”B1991”> Billen, G., C. Lancelot, and M. Meybeck (1991), N, P and Si retention along the aquatic continuum from land to ocean. Ocean Margin Processes in Global Change, R.F.C Mantoura, J.-M. Martin, and R. Wollast, Eds. (John Wiley & Sons Ltd.), pp. 19-44.</ref> also contributes significantly to the budget of this element. <br />
<br />
Riverine Si fluxes, originating predominantly from weathering, have generally been altered little by human activity<ref name="Jickells 1998"/> . <br />
<br />
However, human management of rivers has, in some cases, altered the Si fluxes extensively<ref name=”Humborg2002”> Humborg, C, S. Blomqvist, E. Avsan, Y. Bergensund, E. Smedberg, J. Brink, and C.-M. Morth (2002), Hydrological alterations with river damming in northern Sweden: implications for weathering and river biogeochemistry, Global Biogeochemical Cycles, 16 (3), 1039</ref> , often leading to a reduction in diatom blooms as a result of damming.<br />
<br />
===Groundwater===<br />
<br />
The direct discharge of groundwater into the ocean, termed submarine groundwater discharge (SGD), has been recently recognized as an additional pathway of nutrients from the land to coastal waters <ref name="Johannes1980">Johannes, R.E. (1980), The ecological significance of the submarine discharge of groundwater, Marine Ecology-Progress Series 3, 365-373.</ref> <ref name=”Capone1985”> Capone, D.G., and M.F. Bautista (1985), A groundwater source of nitrate in nearshore marine sediments, Nature 313, 214 216.</ref>, see the article [[Submarine groundwater discharge and its influence on the coastal environment]]. On a global scale, SGD rates vary between 0.01-10 % of river runoff<ref name=”Church1996”>Church, T.H. (1996), An underground route for the water cycle, Nature 380, 579-580.</ref>. However, the concentrations of nutrients in groundwater are typically higher than those in coastal and river waters <ref name="Johannes1980"/> <ref name="Valiela1990">Valiela, I., J. Costa, K. Foreman, J. Teal, B. Howes, and D. Aubrey (1990), Groundwater-borne inputs from watersheds to coastal waters, Biogeochemistry 10, 177-198.</ref> <ref name="Dollar1992">Dollar, S.J., and M.J. Atkinson (1992), Effects of nutrient subsidies from groundwater to nearshore marine ecosystems off the island of Hawaii, Estuarine, Coastal and Shelf Science 35, 409-424.</ref> <ref name="Moore1996">Moore, W.S. (1996), Large groundwater inputs to coastal waters revealed by 226Ra enrichments, Nature 380, 612-614.</ref> <ref name=”Uchiyama2000”>Uchiyama, Y., K. Nadaoka, P. Rolke, K. Adachi, and H. Yagi (2000), Submarine groundwater discharge into the sea and associated nutrient transport in a sandy beach, Water Resources Research 36, 1467-1479.</ref>. Therefore, in terms of fluxes, such high concentrations can compensate for the relatively low SGD rates. At the local scale, SGD of nutrients is a prominent transport pathway, particularly in enclosed bays, [[karstic]] and fractured systems (e.g., Hawaii<ref name="Garison2003">Garrison, G.H., C.R. Glenn, and G.M. McMurty (2003), Measurement of submarine groundwater discharge in Kahana Bay, O’ahu, Hawaii, Limnology and Oceanography 48, 920-928.</ref>), or at locations where rivers are small or non-existent (e.g., Yucatan peninsula<ref name="Hanshaw1980"> Hanshaw, B.B., and W. Back (1980), Chemical mass-wasting of the northern Yucatan Peninsula by groundwater dissolution, Geology 8, 222-224.</ref>).<br />
<br />
===Atmosphere===<br />
<br />
Atmospheric deposition is a significant source of N compounds to the coastal zone, particularly in summer and autumn, but is only a minor source of Si and P<ref name="Conley1993">Conley D.J., C.L. Schelske, and E.F. Stoermer (1993), Modification of the biogeochemical cycle of silica with eutrophication, Marine Ecology-Progress Series 101, 179–192.</ref> <ref name=”Conley2000”>Conley D.J., P. Stalnacke, H. Pitkanen, and A. Wilander (2000), The transport and retention of dissolved silicate by rivers in Sweden and Finland, Limnology and Oceanography 45, 1850–1853.</ref>,<ref name="Jickells 1998"/>. Nitrogen delivered by the atmospheric pathway can be either in the oxidized or reduced form<ref name=”Galloway1995”> Galloway J., W. Chlesinger, H. Levy, A. Michaels, and J. Schnoor (1995), Nitrogen fixaton: Anthropogenic enhancement and environmental response, Global Biogeochemical Cycles 9, 235-252.</ref> . For instance, atmospheric deposition amounts to 30% of the total land based nitrogen input to the North Sea, mainly as oxidized N, and 50% to the Baltic Sea<ref name=”NorthSeaTaskForce1993”> North Sea Task Force (1993), North Sea Quality Status Report, Oslo and Paris Commissions, London. Olsen & Olsen, Fredensborg, Denmark.</ref> . The N:Si:P ratio for wet deposition in the North Sea is 503:2:1<ref name=”Rendell1993”> Rendell, A. R., Ottley, C. J., Jickells, T. D. & Harrison, R. M. Tellus 45, 53−63 (1993).</ref> .<br />
<br />
==Nutrient transformation==<br />
Nutrients are significantly altered by biogeochemical processes during their transport along the land-ocean transition zone, especially in [[Estuaries|estuarine]] systems. Figure 1 summarizes the major N sources and transformation processes in an estuary. Estuaries are usually turbid, and hence primary production is often limited by light availability. Light conditions generally improve towards the [[coastal zone]] and [[primary production]] becomes a dominant process in controlling the biogeochemical cycles of nutrients<ref name="Jickells 1998"/>. <br />
<br />
[[Image:Uses3.jpg|thumb|right| Fig.1. Bioturbated seabed.]]<br />
Sediments cover most of the seabed and hence most of the earth. [[Recycling of carbon and nutrients]] within this habitat (both subtidally and intertidally) is critical both at small and large scales. The availability of essential nutrients, such as nitrogen and phosphorus, and metals is essential for life. Processes that aid nutrient cycling are crucial to ecosystem functioning, as this increases the availability of nutrients and thus maintains productivity of the system. For example, in the marine benthic environment, bioturbation by marine worms, mainly through burrowing in the sediment, moves nutrients from deep sediment layers to the surface and vice versa (Fig. 1). Nutrient cycling is also maintained through processes such as ingestion and excretion of materials by organisms e.g. fish mineralise nitrogen and phosphorus through excretion. <br />
<br />
<br />
===Nitrogen===<br />
N species in aquatic environments include dissolved ([[nitrate]], [[nitrite]], [[ammonium]], [[organic N]]) and particulate (organic N) constituents<ref name="Tappin 2002"> Tappin, A.D. (2002), An Examination of the Fluxes of Nitrogen and Phosphorus in Temperate and Tropical Estuaries: Current Estimates and Uncertainties, Estuarine, Coastal and Shelf Science 55, 885-901. </ref> . The removal of N occurs by deposition and permanent burial in sediments and, most importantly, loss to the atmosphere by bacterial [[denitrification]]. This process is coupled with organic matter decomposition and reduces nitrate to gaseous N<sub>2</sub>/N<sub>2</sub>O under anoxic conditions. Part of the nitrate pool originates from coupled nitrification/denitrification, in which the ammonium produced from organic matter degradation is first oxidized to nitrate, and subsequently denitrified <ref name="Jickells 1998"/>. In temperate and tropical estuaries the estimated loss of nitrate N via denitrification varies widely, and also varies in time and space within estuaries<ref name=”Barnes1998”> Barnes, J., and N.J.P. Owens (1998), Denitrification and nitrous oxide concentrations in the Humber Estuary, UK, and adjacent coastal zones, Marine Pollution Bulletin 37, 247–26.</ref> <ref name=”Dong2000”> Dong, L.F., D.C.O. Thornton, D.B. Nedwell, and G.J.C. Underwood (2000), Denitrification in sediments of the River Colne estuary, England, Marine Ecology Progress Series 203, 109–122.</ref> . Because denitrification requires low oxygen concentrations, this process is particularly important in muddy sediments<ref name=”Seitzinger1998”> Seitzinger, S.P. 1988. Denitrification in freshwater and coastal marine ecosystems: ecological and geochemical importance. Limnology and Oceanography 33:702-724.</ref> <ref name=”Malcolm1997”> Malcolm, S.J. and Sivyer, D.B., 1997. Nutrient recycling in intertidal sediments. in Jickells, T. and Rae, J.E. (Eds) Biogeochemistry of Intertidal Sediments. Cambridge University Press, pp. 59–83.</ref> . It is also quantitatively more important in ecosystems characterized by relatively long residence times<ref name=”Nixon1995”> Nixon, S.W. (1995), Coastal marine eutrophication: A definition, social causes, and future concerns, Ophelia 41, 199–219.</ref> . In groundwater systems, the nitrate supplied either by infiltrating water or produced through nitrification<ref name=”Horrigan1985”> Horrigan, S.G., and Capone, D.G (1985), Rates of nitrification and nitrate reduction in nearshore marine sediments under varying environmental conditons, Marine Chemistry 16, 317-327</ref> <ref name=”Nowicki1999”> Nowicki, B.L., E. Requintina, D. van Keuren, and J. Portnoy (1999), The role of sediment denitrification in reducing groundwater-derived nitrate inputs to Nauset Marsh Estuary, Cape Cod, Massachusetts, Estuaries 22, 245-259.</ref> is also commonly removed through denitrification. As in surface estuaries, a set of conditions, namely the presence of labile organic matter, a low redox potential and sufficient time for reaction, are prerequisite for effective denitrification to occur. However, field studies often report only limited nitrate removal prior to discharge to coastal waters primarily due to a lack of labile dissolved organic matter<ref name=”Star1993”> Starr, R.C., and R.W. Gillham (1993), Denitrification and organic-carbon availability in two aquifers, Ground Water 31, 934–947.</ref> <ref name=”Slater1987”> Slater, J.M., and D.G. Capone (1987), Denitrification in aquifer soil and nearshore marine sediments influenced by groundwater nitrate, Applied and Environmental Microbiology 53, 1292-1297.</ref> <ref name=”DeSimone1996”> DeSimone, L.A., and B.L. Howes (1996), Denitrification and nitrogen transport in a coastal aquifer receiving wastewater discharge, Environmental Science and Technology 30, 1152-1162.</ref>, as is the case in many shallow groundwater aquifers or sandy nearshore sediments, or due to high groundwater velocities<ref name="Capone1990">Capone, D.G., and J.M. Slater (1990), Interannual patterns of water-table height and groundwater derived nitrate in nearshore sediments, Biogeochemistry 10, 277-288.</ref> <ref name=”Giblin1990”> Giblin, A.E., and A.G. Gaines (1990), Nitrogen inputs to a marine embayment: The importance of groundwater, Biogeochemistry 10, 309-328.</ref> .<br />
<br />
===Phosphorus===<br />
<br />
P species in aquatic systems include dissolved (inorganic, organic P) and particulate (inorganic, organic P) constituents<ref name="Tappin 2002"/> . The retention of P in the land-ocean transition zone is often attributed to adsorption on solid particles, which are constantly trapped in estuarine sediments<ref name=”Jickells1991”> Jickells, T.D., T.H. Blackburn, J.O. Blanton, D. Eisma, S.W. Fowler, R.F.C. Manroura, C.S. Martens, A. Moll, R. Scharek, K.I. Suzu, and D. Vaulot (1991), What determines the fate of material within ocean margins? Ocean Margin Processes in Global Change, R.F.C Mantoura, J.-M. Martin, and R. Wollast, Eds. (John Wiley & Sons Ltd.), pp. 211–234.</ref> , or forms part of the solid matrix in coastal aquifers. However, in the case of very large rivers that discharge directly in the continental shelf, P retention in the mixing zones between freshwater and seawater will be limited <ref name=”Milliman1991”> Milliman, J.D. (1991), in Ocean Margin Processes in Global Change, R.F.C Mantoura, J.-M. Martin, and R. Wollast, Eds. (John Wiley & Sons Ltd.), pp. 69–90.</ref> . Adsorption onto solids such as iron and aluminum oxides is particularly effective<ref name=”Krom1980”> Krom, M.D., and R.A. Berner (1980), Adsorption of phosphate in anoxic marine sediments, Limnology and Oceanography 25, 797-806.</ref> <ref name=”Frossard1995”> Frossard, E., M. Brossard, M.J. Hedley, and A. Metherell (1995), Reactions controlling the cycling of P in soils. Phosphorus in the global environment, H. Tiessen, Ed. (John Wiley & Sons Ltd.), pp. 107-138.</ref> , and thus may be also coupled to the redox conditions <ref name=”Spiteri2007”> Spiteri, C., C.P. Slomp, K. Tuncay, and C. Meile (2007), Modeling biogeochemical processes in subterranean estuaries: The effect of flow dynamics and redox conditions on submarine groundwater discharge, Water Resources Research, doi:10.1029/2007WR006071.</ref> . For instance, removal of P is very efficient in subterranean estuaries characterized by zones of [[iron oxide]] accumulation, (“Iron Curtains” <ref name=”Charette2002”> Charette, M.A., and E.R. Sholkovitz (2002), Oxidative precipitation of groundwater-derived ferrous iron in the subterranean estuary of a coastal bay, Geophysical Resources Letters 29, art. no.-1444.</ref> <ref name=”Spiteri2006”> Spiteri, C., P. Regnier, C.P. Slomp, and M.A. Charette (2006), pH-Dependent iron oxide precipitation in a subterranean estuary, Journal of Geochemical Exploration 88, 399-403.</ref> ). The behavior of P in estuarine systems is also influenced by the strong physico-chemical gradients, which result from the variations in pH, ionic strength and solution composition between the freshwater and seawater end-members (e.g. <ref name=”Froelich1998”> Froelich, P.N. (1988), Kinetic control f dissolved phosphate in natural rivers and estuaries: A primer o the phosphate buffer mechanism, Limnology and Oceanography 33, 649-668.</ref> <ref name=”Lebo1991”> Lebo, M.E. (1991), Particle-bound phosphorus along an urbanized coastal plain estuary, Marine Chemistry 34, 225-246.</ref> <ref name=”VadderZee2007”> Van der Zee, C., N. Roevros, and L. Chou (2007), Phosphorus speciation, transformation and retention in the Scheldt estuary (Belgium/The Netherlands) from the freshwater tidal limits to the North Sea, Marine Chemistry doi:10.1016/j.marchem.2007.01.003.</ref> ). The removal of P can occur through bacterial reduction of phosphate to gaseous phosphine. However, little is known on the rate of [[phosphate]]-[[phosphine]] transformation and its contribution to overall P cycling<ref name=”Gassman1994”> Gassman, G. (1994) Phosphine in the fluvial and marine hydrosphere, Marine Chemistry 45, 197–205.</ref> <ref name="Tappin 2002"/> . <br />
<br />
<br />
Tidal and marginal sediments are considered important sinks of N and P, although a quantitative estimation of their role remains uncertain<ref name=”Carpenter1997”> Carpenter, K. (1997) A critical appraisal of the methodology used in studies of material flux between [[saltmarshes]] and coastal waters. Biogeochemistry of Intertidal Sediments, T.D. Jickells, and J.E. Rae, Eds. (Cambridge University Press), pp. 59–83.</ref> <ref name=”Ruddy1998a”> Ruddy, G., C. M. Turley, and T.E.R. Jones (1998a), Ecological interaction and sediment transport on an intertidal mudflat I. Evidence for a biologically mediated sediment-water interface. Sedimentary Processes in the Intertidal Zone, K.S. Black, D.M. Paterson, and A. Cramp, Eds. Geological Society of London Special Publications 139, pp. 135–148.</ref> <ref name=”Ruddy1998b”> Ruddy, G., C.M. Turley, and T.E.R. Jones (1998b), Ecological interaction and sediment transport on an intertidal mudflat II. An experimental dynamic model of the sediment-water interface. Sedimentary Processes in the Intertidal Zone. K.S. Black, D.M. Paterson, and A. Cramp, Eds. Geological Society of London Special Publications 139, pp. 149–166.</ref> . On the global scale, it is generally accepted that intertidal sediments are more efficient for P burial than for N<ref name=”Billen1991”> Billen, G., C. Lancelot, and M. Meybeck (1991), N, P and Si retention along the aquatic continuum from land to ocean. Ocean Margin Processes in Global Change, R.F.C Mantoura, J.-M. Martin, and R. Wollast, Eds. (John Wiley & Sons Ltd.), pp. 19-44.</ref> <ref name=”Howarth1995”> Howarth, R., H. Jensen, R. Marino, and H. Postma, Phosphorus in the Global Environment:Transfers, Cycles and Management, H. Tiessen, Ed., Scientific Committee on Problems of the Environment 54. (Wiley, New York, 1995), pp. 323–356.</ref> .<br />
<br />
===Silicon===<br />
<br />
Relevant Si species in the aquatic environments include dissolved Si (DSi), mainly as undissociated monomeric silicic acid, Si(OH)<sub>4</sub>, and particulate Si (biogeneic [[silica]], BSiO<sub>2</sub>), which includes the amorphous silica in both living biomass and biogenic detritus in surface waters, soils and sediments. The main transformation processes are the uptake of DSi and the biomineralisation as BSiO2 in plants and organisms, as well as the dissolution of BSiO2 back to DSi. Over sufficiently long time scales, BSiO<sub>2</sub> may undergo significant chemical and mineralogical changes<ref name=”VanCappellan2002”> Van Cappellen, P., S. Dixit, and J. van Beusekom (2002), Biogenic silica dissolution in the oceans: Reconciling experimental and field-based dissolution rates, Global Biogeochemical Cycles 16, 1075, doi:10.1029/2001GB001431.</ref> , even including a complete diagenetic transformation of the opaline silica into alumino-silicate minerals <ref name=”Michalopoulos2000”> Michalopoulos, P., R.C. Aller, and R.J. Reeder (2000), Conversion of diatoms to clays during early diagenesis in tropical, continental shelf muds, Geology 28, 1095-1098.</ref>.<br />
<br />
The major producers of BSiO<sub>2</sub> in marine environments are diatoms. However, other organisms such as [[radiolarians]], [[sponges]] and [[chrysophytes]] may be important local sources of BSiO<sub>2</sub><ref name=”Simpson1981”> Simpspon, T.L. and B.E. Volcani (1981), Silicon and Siliceous Structures in Biological Systems, Springer-Verlag NY, 587 pp </ref> . Large quantities of DSi are also fixed on land by higher plants, forming amorphous silica deposits, known as [[phytoliths]]<ref name=”Piperno1998”> Piperno, D.L. (1998), Phytolith analysis. An archaeological and geological perspective. London: Academic Press.</ref> . Their role in the Si cycle has only recently been studied<ref name=”Bartoli1983”> Bartoli, F. (1983), The biogeochemical cycle of silicon in two temperate forest ecosystems, Ecological Bulletins (Stockholm) 35, 469–476.</ref> <ref name=”Meunier1999”> Meunier, J.D., F. Colin, and C. Alarcon (1999), Biogenic silica storage in soils, Geology 27, 835-838. </ref> . In general, riverine Si fluxes have been much less altered by human activity than those of N and P. However, increased damming of major rivers has promoted siliceous phytoplankton blooms<ref name=”Billen1991”> Billen, G., C. Lancelot, and M. Meybeck (1991), N, P and Si retention along the aquatic continuum from land to ocean </ref> <ref name="Humborg1997"> Humborg, C., V. Ittekot, A. Cociosu, and B. v. Bdungen (1997), Effect of Danube River dam on Black Sea biogeochemistry and ecosystem structure, Nature 386, 385 – 388.</ref> , and therefore, reduced Si fluxes to the coastal zone. For example, the damming of the Danube has reduced the DSi concentration by more than 50%<ref name="Humborg1997"/>.<br />
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==See also==<br />
Articles in the [[:Category:Eutrophication]].<br />
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<br />
==External links==<br />
:[http://www.eloisegroup.org/themes/nutrients/contents.htm ELOISE Nutrient Dynamics in European Water Systems ONLINE]<br />
:[http://www.eloisegroup.org/themes/nutrients/pdf/nutrient_dynamics.pdf ELOISE Nutrient Dynamics in European Water Systems in pdf format]<br />
:[http://www.eloisegroup.org/themes/nutrients/casesintro.htm Case studies]<br />
:[http://www.loicz.org/ LOICZ Land-Ocean Interactions in the Coastal Zone]<br />
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==References==<br />
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{{author<br />
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|AuthorFullName=Pierre Regnier<br />
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|AuthorFullName=Claudette Spiteri<br />
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[[Category:Coastal and marine ecosystems]] <br />
[[Category:Coastal and marine pollution]]<br />
[[Category:Eutrophication]]</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=What_causes_eutrophication%3F&diff=76211What causes eutrophication?2019-12-04T19:32:26Z<p>Dronkers J: </p>
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[[Image:SewageEffluentDenver.jpg|350px|thumb|right|<small>Discharge of Denver sewage treatment plant in the Platte River (USA). Photo credit: Jeffrey Beall (2008)</small>]]<br />
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<P ALIGN="justify">[[Eutrophication]] is the (mostly undesired) increase in the concentration of [[Nutrient|nutrients]] to an ecosystem. Increased nutrient enrichment can arise from both '''point''' and '''non-point sources''':</P><br />
* '''Point source pollution''': Pollution that comes from contaminants that enter a waterway from a single identifiable source such as stationary locations or fixed facilities. Examples are discharges from a sewage treatment plant or industrial plants and fish farms.<br />
* '''Non-point source pollution''': Pollution from widespread including human activities with no specific point of discharge or entry into receiving watercourses. Examples are leaching out of nitrogen compounds from fertilized agricultural lands and losses from atmospheric deposition.<br />
[[Image:manure_run-off.jpg|350px|right|thumb|<small>Manure run-off, an example of non-point source pollution (Photo credit: Chris Court)</small>]]<br />
<P ALIGN="justify"><br />
The enrichment of water by nutrients can be of a '''natural origin''' (natural eutrophication) but is often dramatically increased by '''human activities''' (cultural or [[Anthropogenic|anthropogenic]] eutrophication). '''Natural eutrophication''' has been occurring for millennia. It is the process of addition, flow and accumulation of nutrients to water bodies resulting in changes to the [[primary production]] and species composition of the community. '''Cultural eutrophication''' is the process that speeds up natural eutrophication because of human activity. There are three main sources of anthropogenic nutrient input: erosion and leaching from fertilized agricultural areas, and sewage from cities and industrial waste water. Atmospheric deposition of nitrogen (from animal breeding and combustion gases) can also be important.</P><br />
<P ALIGN="justify"><br />
The most common nutrients causing eutrophication are [[nitrogen]] and [[phosphorus]]. The main source of nitrogen pollutants is run-off from agricultural land, whereas most phosphorus pollution comes from households and industry, including phosphorus-based detergents. These nutrients enter aquatic ecosystems via the air, surface water or groundwater. Most of the commercially fixed nitrogen and mined phosphorus goes into production of [[fertilizer]]. The rising demand for fertilizer has come from the need to meet the nutritional demands of our rapidly expanding human population. The rise in intensive fertilizer use has serious implications for coastal habitats because greater application results in greater runoff, and the fraction of fertilizer lost from fields will increase with intensity of application. Increased global production of nitrogenous fertilizers have largely been linked to concerns over the relationship between water quality and eutrophication. Nutrient removal in sewage treatment plants and promotion of phosphorus-free detergents are vital to minimize the impact of nitrogen and phosphorus pollution in Europe's waters.</P><br />
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'''Related articles'''<br />
* [[Continental Nutrient Sources and Nutrient Transformation]]<br />
* [[Threats to the coastal zone]]<br />
* Other articles in the [[:Category:Eutrophication]].<br />
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'''References'''<br />
<P ALIGN="justify"><br />
# Causes, historical development, effects and future challenges of a common environmental problem: eutrophication. De Jonge, V.N.; Elliot, M.; Orive, E. (2002). ''Hydrobiologia 475-476'':1-19.<br />
# Source apportionment of nitrogen and phosphorus inputs into the aquatic environment. European Environment Agency (2005). ''EEA Report'', 7 Office for Official Publications of the European Communities: Luxembourg. ISBN 92-9167-777-9.48 pp.<br />
# Eutrophication and health. European Commission (2002). Office for Official Publications of the European Communities: Luxembourg. ISBN 92-894-4413-4.28 pp.</P><br />
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[[Category:Eutrophication]]</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Possible_consequences_of_eutrophication&diff=76210Possible consequences of eutrophication2019-12-04T19:24:45Z<p>Dronkers J: </p>
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==Introduction==<br />
<P ALIGN="justify"><br />
Enhanced plant production and improved fish yields are sometimes described as positive impacts of [[Eutrophication|eutrophication]], especially in countries where fish and other aquatic organisms are a significant source of food. However detrimental ecological impacts can in turn have other negative consequences and impacts which are described below. Essentially the entire aquatic [[ecosystem]] changes with eutrophication. The diagram below gives an overview on the eutrophication process and its causes and consequences. </P><br />
[[Image:eutrocon.png|705|center]]<br />
<br />
==Ecological impacts==<br />
==== Increased biomass of phytoplankton resulting in [[algal bloom]]s ====<br />
[[Image:Plentiful_plankton.jpg|175px|thumb|right|<small>Envisat satellite image of an algal bloom captured with MERIS (Photo Credit: ESA, 2009)</small>]]<br />
<P ALIGN="justify">[[Phytoplankton]] or microalgae are [[photosynthesizing]] microscopic organisms. They contain chlorophyll and require sunlight in order to live and grow. Most phytoplankton are buoyant and float in the upper part of the ocean where sunlight penetrates the water. In a balanced ecosystem they provide food for a wide range of organisms such as whales, shrimp, snails and jellyfish.<br />
Among the more important groups are the diatoms, cyanobacteria, dinoflagellates and coccolithophores (see: [[Marine Plankton]]). <br />
Phytoplankton species require inorganic [[Nutrient|nutrients]] such as nitrates, phosphates, and sulfur which they convert into proteins, fats and carbohydrates. When '''too many''' of these '''nutrients''' (by natural or [[Anthropogenic|anthropogenic]] cause) are available in the water phytoplankton may grow and multiply very fast forming [[Algal_bloom | algal blooms]]. Algal blooms may occur in freshwater as well as marine environments. Only one or a small number of phytoplankton species are involved and some blooms discolor (green, yellow-brown or red) the water due to their high density of pigmented cells. Blooms in the ocean may cover a large area and are easily visible in '''satellite images'''.</P><br />
==== Toxic or inedible phytoplankton species (harmful algal blooms)====<br />
<P ALIGN="justify">'''[[Harmful_algal_bloom | Harmful algal blooms (HAB)]]''' are bloom events involving '''toxic or harmful phytoplankton'''. These cause harm through the production of toxins or by their accumulated biomass, which can effect co-occurring organisms and alter food web dynamics. Impacts include:</P><br />
*Human illness,<br />
*Mortality of fish, birds and mammals following consumption or indirect exposure to HAB toxins,<br />
*Substantially economic losses to coastal communities and commercial fisheries.<br />
<br />
==== Increased blooms of gelatinous zooplankton====<br />
<P ALIGN="justify">[[Phytoplankton]] are the food source for numerous other organisms, especially the zooplankton. [[Zooplankton]] are heterotrophic plankton. They are primarily transported by ambient water currents but many have locomotion. Through their consumption and processing of phytoplankton and other food sources they play a role in aquatic food webs as a resource for higher trophic levels including fish. Zooplankton can be divided in two important groups: crustacean (copepods and krill) and '''gelatinous zooplankton'''. Gelatinous zooplankton have relatively fragile, plastic gelatinous bodies that contain at least 95% water and which lack rigid skeletal parts. The most well-known are the jellyfish. Eutrophication is believed to cause an '''increase''' in the relative importance of '''gelatinous''' versus crustacean '''zooplankton'''. On many areas of the world where the natural species diversity has been affected by pollution, over-fishing and climate change gelatinous zooplankton organisms may be becoming the dominant species.</P><br />
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==== Decreases in water transparency (increased turbidity)====<br />
<P ALIGN="justify">The growth of phytoplankton can cause increased [[Turbidity|turbidity]] or decreased penetration of light into the lower depths of the water column. In lakes and rivers this can inhibit growth of submerged aquatic plants and affect species which are dependent on them (fish, shellfish).</P><br />
<br />
==== Dissolved oxygen depletion or hypoxia resulting in increased incidences of fish kills and / or dead benthic animals====<br />
[[Image:FishKill.jpg|160px|thumb|right|<small>A menhaden fish kill due severe hypoxia (Photo credit: Chris Deacutis, IAN Image library )</small>]]<br />
<P ALIGN="justify">Oxygen is required for all life forms on the planet. Oxygen is produced by plants during ([[photosynthesis]]). At night animals and plants, as well as aerobic micro-organisms and decomposing dead organisms respire and so consume oxygen which results in a decrease in dissolved oxygen levels. Large fluctuations in dissolved oxygen levels may be the result of an [[algal bloom]]. While the algae population is growing at a fast rate, dissolved oxygen levels decrease. When these algae die, they are decomposed by bacteria which consume oxygen in this process so that the water can become temporarily hypoxic. Oxygen depletion, or [[Hypoxia|hypoxia]], is a common effect of eutrophication in water. The '''direct effects''' of hypoxia include '''fish kills''', especially the death of fish that need high levels of dissolved oxygen. Changes in fish communities may have an impact on the whole aquatic ecosystem and may deplete fish stocks. In extreme cases hypoxic conditions promote the growth of bacteria that produce toxins deadly to birds and animals. Zones where this occurs are called [[Case_studies_eutrophication#Ecological_impacts_of_eutrophication_.28Case_study:_Eutrophication_and_dead_zones.29|dead zones]].</P><br />
<br />
==== Species biodiversity decreases and the dominant biota changes====<br />
<P ALIGN="justify">Eutrophication leads to changes in the availability of light and certain nutrients to an ecosystem. This causes shifts in the species composition so that only the more tolerant species survive and new competitive species invade and out-compete original inhabitants. Examples are macroalgae and their massive biomass which inhibits the growth of other aquatic plants and algal blooms that consists of one type of phytoplankton species because other species are expelled.</P><br />
<br />
==== Increased biomass of macroalgae====<br />
<P ALIGN="justify">Algal blooms may also consist of '''marine seaweeds''' or '''macroalgae'''. These blooms are recognizable by large blades of algae that may wash up into the shoreline. The seaweed is harmless when it is alive, but when decomposed by anaerobic bacteria toxic gases (such as the colorless hydrogen sulfide (H<sub>2</sub>S)) can be released.</P><br />
<br />
==Human health impacts==<br />
<P ALIGN="justify">Harmful algal bloom species have the capacity to produce '''toxins''' dangerous to humans. Algal [[Toxic|toxins]] are observed in marine ecosystems where they can accumulate in shellfish and more generally in seafood reaching dangerous levels for human as well as animal health. Examples include paralytic, neurotoxic and diarrhoeic shellfish poisoning. Several algal species able of producing toxins harmful to human or marine life have been identified in European coastal waters. The table gives an overview of some species that are regularly observed and represent a risk for seafood consumers.</P><br />
{|border="1" align=center cellspacing="0" cellpadding = "8" width="825px"<br />
!style="background-color:#398C9D" |'''Disease'''<br />
!style="background-color:#398C9D" |'''Symptoms'''<br />
!style="background-color:#398C9D" |'''Species'''<br />
!style="background-color:#398C9D" |'''Carriers''' <br />
|-<br />
| '''A'''mnesic '''s'''hellfish '''p'''oisoning (ASP)<br />
| Mental confusion and memory loss, disorientation and sometimes coma<br />
| Diatoms of the genus [http://www.marinespecies.org/aphia.php?p=taxdetails&id=149045 ''Nitzschia'']<br />
| Shellfish (mussels)<br />
|- <br />
| '''N'''eurotoxic '''s'''hellfish '''p'''oisoning (NSP)<br />
| Muscular paralysis, state of shock and sometimes death<br />
| Genus [http://www.marinespecies.org/aphia.php?p=taxdetails&id=109475 ''Gymnodinium'']<br />
| Oysters, clams and crustaceans<br />
|-<br />
| '''V'''enerupin '''s'''hellfish '''p'''oisoning (VSP)<br />
| Gastrointestinal, nervous and hemorrhagic, hepatic symptoms and in extreme causes delirium and hepatic coma<br />
| Genus [http://www.marinespecies.org/aphia.php?p=taxdetails&id=109566 ''Prorocentrum'']<br />
| Oysters and clams<br />
|-<br />
| '''D'''iarrhoeic '''s'''hellfish '''p'''oisoning (DSP)<br />
| Gastrointestinal symptoms (diarrhoea, vomiting and abdominal pain)<br />
| Genus [http://www.marinespecies.org/aphia.php?p=taxdetails&id=109462 ''Dinophysis''] and [http://www.marinespecies.org/aphia.php?p=taxdetails&id=109566 ''Prorocentrum'']<br />
| Filtering shellfish (oysters, mussels and clams)<br />
|-<br />
| '''P'''aralytic '''s'''hellfish '''p'''oisoning (PSP)<br />
| Muscular paralysis, difficulty in breathing, shock and in extreme causes death by respiratory arrest<br />
| Genus [http://www.marinespecies.org/aphia.php?p=taxdetails&id=109470 ''Alexandrium''] and [http://www.marinespecies.org/aphia.php?p=taxdetails&id=109475 ''Gymnodinium'']<br />
| Oysters, mussels, crustacean and fish<br />
|-<br />
|}<br />
<P ALIGN="justify">Other marine mammals can be vectors for toxins, as in the case of ciguatera, where it is typically predator fish whose flesh is contaminated with the toxins originally produced by dinoflagellates and then poison humans. Symptoms include gastrointestinal and neurological effects.</P><br />
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==Socio-economic impacts==<br />
Nearly all of the above described impacts have a direct or indirect socio-economic impact.<br />
==== Impact on recreation and tourism ====<br />
<P ALIGN="justify">The enrichment of nutrients to an ecosystem can result in a massive growth of macroalgae. The existence of such dense algal growth areas can inhibit or prevent access to waterways. This decreases the fitness for '''use of the water for water sports''' (swimming, boating and fishing).</P><br />
==== Aesthetic impacts====<br />
[[Image:Beach_closed.jpg|200px|thumb|right|<small>As a result of toxic algal blooms beaches can be closed (Photo credit: Elizabeth Halliday, Woods Hole Oceanographic Institution)</small>]]<br />
Algal blooms are unsightly and can have unpleasant smells for example:<br />
* The appearance of a '''white yellowish foam''' on the beach in spring, for example on the shores along the North Sea. The foam is formed by the wind that sweeps up the decaying remains of ''Phaeocystis'' algal colonies. An extreme case is shown in [[Foam beach, Sydney]].<br />
* When macroalgae or seaweed are decomposed by anaerobic bacteria hydrogen sulfide is (H<sub>2</sub>S) released. This gas is characterized by a very unpleasant characteristic foul odor of rotten eggs.<br />
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==== Economical impacts====<br />
<P ALIGN="justify">In some specific cases local authorities must rely on eutrophic waters for production of drinking water. Infected waters increases the '''costs of water treatment''' in order to avoid taste, odor and toxin problems in the water. Due to the toxins produced by harmful algal blooms commercial fish and shellfish may become '''unsuitable for consumption''' resulting in potential economical and financial problems for the fishing industries. In extreme cases beaches are closed due to the presence of toxic algal blooms.</P><br />
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==Related articles==<br />
* [[Threats to the coastal zone]]<br />
* [[Coupled hydrodynamic - water quality - ecological modelling]]<br />
* Articles in the [[:Category:Eutrophication]] <br />
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== References==<br />
#Eutrophication and health. European Commission (2002). Office for Official Publications of the European Communities: Luxembourg. ISBN 92-894-4413-4.28 pp.<br />
#The National Eutrophication monitoring Programme Implementation Manual (Murray et al., 2002).<br />
#Guiry, Michael D. (2013). Nitzschia Hassall, 1845. In: Guiry, M.D. & Guiry, G.M. (2013). AlgaeBase. World-wide electronic publication, National University of Ireland, Galway. Accessed through: World Register of Marine Species at http://www.marinespecies.org/aphia.php?p=taxdetails&id=149045 on 2013-04-22.<br />
#Guiry, Michael D. (2013). Gymnodinium Stein, 1878. In: Guiry, M.D. & Guiry, G.M. (2013). AlgaeBase. World-wide electronic publication, National University of Ireland, Galway. Accessed through: World Register of Marine Species at http://www.marinespecies.org/aphia.php?p=taxdetails&id=109475 on 2013-04-22.<br />
#Guiry, Michael D. (2013). Prorocentrum Ehrenberg, 1834. In: Guiry, M.D. & Guiry, G.M. (2013). AlgaeBase. World-wide electronic publication, National University of Ireland, Galway. Accessed through: World Register of Marine Species at http://www.marinespecies.org/aphia.php?p=taxdetails&id=109566 on 2013-04-22.<br />
#WoRMS (2013). Dinophysis Ehrenberg, 1839. In: Guiry, M.D. & Guiry, G.M. (2013). AlgaeBase. World-wide electronic publication, National University of Ireland, Galway. Accessed through: World Register of Marine Species at http://www.marinespecies.org/aphia.php?p=taxdetails&id=109462 on 2013-04-22.<br />
#Guiry, Michael D.; Moestrup, Ø. (2013). Alexandrium Halim, 1960. In: Guiry, M.D. & Guiry, G.M. (2013). AlgaeBase. World-wide electronic publication, National University of Ireland, Galway. Accessed through: World Register of Marine Species at http://www.marinespecies.org/aphia.php?p=taxdetails&id=109470 on 2013-04-22.<br />
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{{author <br />
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[[Category:Eutrophication]]</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Continental_Nutrient_Sources_and_Nutrient_Transformation&diff=76209Continental Nutrient Sources and Nutrient Transformation2019-12-04T19:22:31Z<p>Dronkers J: </p>
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Nutrients in coastal environments come from various sources - through rivers, groundwater or atmospheric deposition. The main species - Nitrogen, Phosphorus and Silicon - undergo different transformation processes and states. <br />
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==Continental nutrient sources==<br />
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===Rivers===<br />
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On a global scale, riverine inputs of N and P to coastal seas have possibly increased by factors of 2 to 3 <ref name=”Howarth”>Howarth, R., H. Jensen, R. Marino, and H. Postma, in Phosphorus in the Global Environment:Transfers, Cycles and Management, H. Tiessen, Ed., Scientific Committee on Problems of the Environment 54. (Wiley, New York, 1995), pp. 323–356.</ref> ,<ref name=”Duce”> Duce, R., P.S. Liss, J.T. Merrill, E.L. Atlas, P. Buat-Menard, B.B. Hicks, J.M. Miller, J.M. Prospero, R. Arimoto, T.M. Church,. W. Ellis, J.N. Galloway, L. Hansen, T.D. Jickells, A.H. Knap, K.H. Reinhardt, B. Schneider, A. Soudine, J.J. Tokos, S. Tsunogai, R. Wollast, and M. Zhou (1991), The atmospheric input of trace species to the world ocean, Global Biogeochemical Cycles 5, 193-296.</ref> ,<ref name="Jickells 1998">Jickells T.D. (1998), Nutrient Biogeochemistry of the Coastal Zone, Science, 281 217 – 222</ref>. Agriculture, in the form of fertilizers, leachates and animal wastes, is the largest contributor of N and P in aquatic systems <ref name=”Howarth”>Howarth, R., H. Jensen, R. Marino, and H. Postma, in Phosphorus in the Global Environment:Transfers, Cycles and Management, H. Tiessen, Ed., Scientific Committee on Problems of the Environment 54. (Wiley, New York, 1995), pp. 323–356.</ref> . Other major inputs include point-source discharges of wastewater from urban sewer networks<ref name=”B&G2007”> Billen, G., J. Garnier, J. Nemery, M. Sebilo, A. Sferratore, S. Barles, P. Benoit, and M. Benoit (2007), A long-term view of nutrient transfers through the Seine river continuum, Science of the Total Environment 375, 80-97.</ref> ,<ref name=”EEA1999”> European Environment Agency (1999), Nutrients in European Ecosystems. Environmental Assessment Report No. 4, Office for Official Publications of the European Communities, Luxembourg, pp. 156.</ref> and industrial wastes. The direct discharge of P exchanged with soils and sediments<ref name=”B1991”> Billen, G., C. Lancelot, and M. Meybeck (1991), N, P and Si retention along the aquatic continuum from land to ocean. Ocean Margin Processes in Global Change, R.F.C Mantoura, J.-M. Martin, and R. Wollast, Eds. (John Wiley & Sons Ltd.), pp. 19-44.</ref> also contributes significantly to the budget of this element. <br />
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Riverine Si fluxes, originating predominantly from weathering, have generally been altered little by human activity<ref name="Jickells 1998"/> . <br />
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However, human management of rivers has, in some cases, altered the Si fluxes extensively<ref name=”Humborg2002”> Humborg, C, S. Blomqvist, E. Avsan, Y. Bergensund, E. Smedberg, J. Brink, and C.-M. Morth (2002), Hydrological alterations with river damming in northern Sweden: implications for weathering and river biogeochemistry, Global Biogeochemical Cycles, 16 (3), 1039</ref> , often leading to a reduction in diatom blooms as a result of damming.<br />
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===Groundwater===<br />
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The direct discharge of groundwater into the ocean, termed submarine groundwater discharge (SGD), has been recently recognized as an additional pathway of nutrients from the land to coastal waters<ref name="Johannes1980">Johannes, R.E. (1980), The ecological significance of the submarine discharge of groundwater, Marine Ecology-Progress Series 3, 365-373.</ref>,<ref name=”Capone1985”> Capone, D.G., and M.F. Bautista (1985), A groundwater source of nitrate in nearshore marine sediments, Nature 313, 214 216.</ref>. On a global scale, SGD rates vary between 0.01-10 % of river runoff<ref name=”Church1996”>Church, T.H. (1996), An underground route for the water cycle, Nature 380, 579-580.</ref>. However, the concentrations of nutrients in groundwater are typically higher than those in coastal and river waters<ref name="Johannes1980"/>,<ref name="Valiela1990">Valiela, I., J. Costa, K. Foreman, J. Teal, B. Howes, and D. Aubrey (1990), Groundwater-borne inputs from watersheds to coastal waters, Biogeochemistry 10, 177-198.</ref>,<ref name="Dollar1992">Dollar, S.J., and M.J. Atkinson (1992), Effects of nutrient subsidies from groundwater to nearshore marine ecosystems off the island of Hawaii, Estuarine, Coastal and Shelf Science 35, 409-424.</ref>,<ref name="Moore1996">Moore, W.S. (1996), Large groundwater inputs to coastal waters revealed by 226Ra enrichments, Nature 380, 612-614.</ref>,<ref name=”Uchiyama2000”>Uchiyama, Y., K. Nadaoka, P. Rolke, K. Adachi, and H. Yagi (2000), Submarine groundwater discharge into the sea and associated nutrient transport in a sandy beach, Water Resources Research 36, 1467-1479.</ref>. Therefore, in terms of fluxes, such high concentrations can compensate for the relatively low SGD rates. At the local scale, SGD of nutrients is a prominent transport pathway, particularly in enclosed bays, [[karstic]] and fractured systems (e.g., Hawaii<ref name="Garison2003">Garrison, G.H., C.R. Glenn, and G.M. McMurty (2003), Measurement of submarine groundwater discharge in Kahana Bay, O’ahu, Hawaii, Limnology and Oceanography 48, 920-928.</ref>), or at locations where rivers are small or non-existent (e.g., Yucatan peninsula<ref name="Hanshaw1980"> Hanshaw, B.B., and W. Back (1980), Chemical mass-wasting of the northern Yucatan Peninsula by groundwater dissolution, Geology 8, 222-224.</ref>).<br />
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===Atmosphere===<br />
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Atmospheric deposition is a significant source of N compounds to the coastal zone, particularly in summer and autumn, but is only a minor source of Si and P<ref name="Conley1993">Conley D.J., C.L. Schelske, and E.F. Stoermer (1993), Modification of the biogeochemical cycle of silica with eutrophication, Marine Ecology-Progress Series 101, 179–192.</ref>,<ref name=”Conley2000”>Conley D.J., P. Stalnacke, H. Pitkanen, and A. Wilander (2000), The transport and retention of dissolved silicate by rivers in Sweden and Finland, Limnology and Oceanography 45, 1850–1853.</ref>,<ref name="Jickells 1998"/>. Nitrogen delivered by the atmospheric pathway can be either in the oxidized or reduced form<ref name=”Galloway1995”> Galloway J., W. Chlesinger, H. Levy, A. Michaels, and J. Schnoor (1995), Nitrogen fixaton: Anthropogenic enhancement and environmental response, Global Biogeochemical Cycles 9, 235-252.</ref> . For instance, atmospheric deposition amounts to 30% of the total land based nitrogen input to the North Sea, mainly as oxidized N, and 50% to the Baltic Sea<ref name=”NorthSeaTaskForce1993”> North Sea Task Force (1993), North Sea Quality Status Report, Oslo and Paris Commissions, London. Olsen & Olsen, Fredensborg, Denmark.</ref> . The N:Si:P ratio for wet deposition in the North Sea is 503:2:1<ref name=”Rendell1993”> Rendell, A. R., Ottley, C. J., Jickells, T. D. & Harrison, R. M. Tellus 45, 53−63 (1993).</ref> .<br />
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==Nutrient transformation==<br />
Nutrients are significantly altered by biogeochemical processes during their transport along the land-ocean transition zone, especially in [[Estuaries|estuarine]] systems. Figure 1 summarizes the major N sources and transformation processes in an estuary. Estuaries are usually turbid, and hence primary production is often limited by light availability. Light conditions generally improve towards the [[coastal zone]] and [[primary production]] becomes a dominant process in controlling the biogeochemical cycles of nutrients<ref name="Jickells 1998"/>. <br />
<br />
[[Image:Uses3.jpg|thumb|right| Fig.1. Bioturbated seabed.]]<br />
Sediments cover most of the seabed and hence most of the earth. [[Recycling of carbon and nutrients]] within this habitat (both subtidally and intertidally) is critical both at small and large scales. The availability of essential nutrients, such as nitrogen and phosphorus, and metals is essential for life. Processes that aid nutrient cycling are crucial to ecosystem functioning, as this increases the availability of nutrients and thus maintains productivity of the system. For example, in the marine benthic environment, bioturbation by marine worms, mainly through burrowing in the sediment, moves nutrients from deep sediment layers to the surface and vice versa (Fig. 1). Nutrient cycling is also maintained through processes such as ingestion and excretion of materials by organisms e.g. fish mineralise nitrogen and phosphorus through excretion. <br />
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===Nitrogen===<br />
N species in aquatic environments include dissolved ([[nitrate]], [[nitrite]], [[ammonium]], [[organic N]]) and particulate (organic N) constituents<ref name="Tappin 2002"> Tappin, A.D. (2002), An Examination of the Fluxes of Nitrogen and Phosphorus in Temperate and Tropical Estuaries: Current Estimates and Uncertainties, Estuarine, Coastal and Shelf Science 55, 885-901. </ref> . The removal of N occurs by deposition and permanent burial in sediments and, most importantly, loss to the atmosphere by bacterial [[denitrification]]. This process is coupled with organic matter decomposition and reduces nitrate to gaseous N<sub>2</sub>/N<sub>2</sub>O under anoxic conditions. Part of the nitrate pool originates from coupled nitrification/denitrification, in which the ammonium produced from organic matter degradation is first oxidized to nitrate, and subsequently denitrified <ref name="Jickells 1998"/>. In temperate and tropical estuaries the estimated loss of nitrate N via denitrification varies widely, and also varies in time and space within estuaries<ref name=”Barnes1998”> Barnes, J., and N.J.P. Owens (1998), Denitrification and nitrous oxide concentrations in the Humber Estuary, UK, and adjacent coastal zones, Marine Pollution Bulletin 37, 247–26.</ref> ,<ref name=”Dong2000”> Dong, L.F., D.C.O. Thornton, D.B. Nedwell, and G.J.C. Underwood (2000), Denitrification in sediments of the River Colne estuary, England, Marine Ecology Progress Series 203, 109–122.</ref> . Because denitrification requires low oxygen concentrations, this process is particularly important in muddy sediments<ref name=”Seitzinger1998”> Seitzinger, S.P. 1988. Denitrification in freshwater and coastal marine ecosystems: ecological and geochemical importance. Limnology and Oceanography 33:702-724.</ref> ,<ref name=”Malcolm1997”> Malcolm, S.J. and Sivyer, D.B., 1997. Nutrient recycling in intertidal sediments. in<br />
Jickells, T. and Rae, J.E. (Eds) Biogeochemistry of Intertidal Sediments. Cambridge University Press, pp. 59–83.</ref> . It is also quantitatively more important in ecosystems characterized by relatively long residence times<ref name=”Nixon1995”> Nixon, S.W. (1995), Coastal marine eutrophication: A definition, social causes, and future concerns, Ophelia 41, 199–219.</ref> . In groundwater systems, the nitrate supplied either by infiltrating water or produced through nitrification<ref name=”Horrigan1985”> Horrigan, S.G., and Capone, D.G (1985), Rates of nitrification and nitrate reduction in nearshore marine sediments under varying environmental conditons, Marine Chemistry 16, 317-327</ref> ,<ref name=”Nowicki1999”> Nowicki, B.L., E. Requintina, D. van Keuren, and J. Portnoy (1999), The role of sediment denitrification in reducing groundwater-derived nitrate inputs to Nauset Marsh Estuary, Cape Cod, Massachusetts, Estuaries 22, 245-259.</ref> is also commonly removed through denitrification. As in surface estuaries, a set of conditions, namely the presence of labile organic matter, a low redox potential and sufficient time for reaction, are prerequisite for effective denitrification to occur. However, field studies often report only limited nitrate removal prior to discharge to coastal waters primarily due to a lack of labile dissolved organic matter<ref name=”Star1993”> Starr, R.C., and R.W. Gillham (1993), Denitrification and organic-carbon availability in two aquifers, Ground Water 31, 934–947.</ref> ,<ref name=”Slater1987”> Slater, J.M., and D.G. Capone (1987), Denitrification in aquifer soil and nearshore marine sediments influenced by groundwater nitrate, Applied and Environmental Microbiology 53, 1292-1297.</ref> ,<ref name=”DeSimone1996”> DeSimone, L.A., and B.L. Howes (1996), Denitrification and nitrogen transport in a coastal aquifer receiving wastewater discharge, Environmental Science and Technology 30, 1152-1162.</ref>, as is the case in many shallow groundwater aquifers or sandy nearshore sediments, or due to high groundwater velocities<ref name="Capone1990">Capone, D.G., and J.M. Slater (1990), Interannual patterns of water-table height and groundwater derived nitrate in nearshore sediments, Biogeochemistry 10, 277-288.</ref>,<ref name=”Giblin1990”> Giblin, A.E., and A.G. Gaines (1990), Nitrogen inputs to a marine embayment: The importance of groundwater, Biogeochemistry 10, 309-328.</ref> .<br />
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===Phosphorus===<br />
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P species in aquatic systems include dissolved (inorganic, organic P) and particulate (inorganic, organic P) constituents<ref name="Tappin 2002"/> . The retention of P in the land-ocean transition zone is often attributed to adsorption on solid particles, which are constantly trapped in estuarine sediments<ref name=”Jickells1991”> Jickells, T.D., T.H. Blackburn, J.O. Blanton, D. Eisma, S.W. Fowler, R.F.C. Manroura, C.S. Martens, A. Moll, R. Scharek, K.I. Suzu, and D. Vaulot (1991), What determines the fate of material within ocean margins? Ocean Margin Processes in Global Change, R.F.C Mantoura, J.-M. Martin, and R. Wollast, Eds. (John Wiley & Sons Ltd.), pp. 211–234.</ref> , or forms part of the solid matrix in coastal aquifers. However, in the case of very large rivers that discharge directly in the continental shelf, P retention in the mixing zones between freshwater and seawater will be limited<ref name=”Milliman1991”> Milliman, J.D. (1991), in Ocean Margin Processes in Global Change, R.F.C Mantoura, J.-M. Martin, and R. Wollast, Eds. (John Wiley & Sons Ltd.), pp. 69–90.</ref> . Adsorption onto solids such as iron and aluminum oxides is particularly effective<ref name=”Krom1980”> Krom, M.D., and R.A. Berner (1980), Adsorption of phosphate in anoxic marine sediments, Limnology and Oceanography 25, 797-806.</ref> ,<ref name=”Frossard1995”> Frossard, E., M. Brossard, M.J. Hedley, and A. Metherell (1995), Reactions controlling the cycling of P in soils. Phosphorus in the global environment, H. Tiessen, Ed. (John Wiley & Sons Ltd.), pp. 107-138.</ref> , and thus may be also coupled to the redox conditions<ref name=”Spiteri2007”> Spiteri, C., C.P. Slomp, K. Tuncay, and C. Meile (2007), Modeling biogeochemical processes in subterranean estuaries: The effect of flow dynamics and redox conditions on submarine groundwater discharge, Water Resources Research, doi:10.1029/2007WR006071.</ref> . For instance, removal of P is very efficient in subterranean estuaries characterized by zones of [[iron oxide]] accumulation, (“Iron Curtains” <ref name=”Charette2002”> Charette, M.A., and E.R. Sholkovitz (2002), Oxidative precipitation of groundwater-derived ferrous iron in the subterranean estuary of a coastal bay, Geophysical Resources Letters 29, art. no.-1444.</ref> ,<ref name=”Spiteri2006”> Spiteri, C., P. Regnier, C.P. Slomp, and M.A. Charette (2006), pH-Dependent iron oxide precipitation in a subterranean estuary, Journal of Geochemical Exploration 88, 399-403.</ref> ). The behavior of P in estuarine systems is also influenced by the strong physico-chemical gradients, which result from the variations in pH, ionic strength and solution composition between the freshwater and seawater end-members (e.g. <ref name=”Froelich1998”> Froelich, P.N. (1988), Kinetic control f dissolved phosphate in natural rivers and estuaries: A primer o the phosphate buffer mechanism, Limnology and Oceanography 33, 649-668.</ref> ,<ref name=”Lebo1991”> Lebo, M.E. (1991), Particle-bound phosphorus along an urbanized coastal plain estuary, Marine Chemistry 34, 225-246.</ref> ,<ref name=”VadderZee2007”> Van der Zee, C., N. Roevros, and L. Chou (2007), Phosphorus speciation, transformation and retention in the Scheldt estuary (Belgium/The Netherlands) from the freshwater tidal limits to the North Sea, Marine Chemistry doi:10.1016/j.marchem.2007.01.003.</ref> ). The removal of P can occur through bacterial reduction of phosphate to gaseous phosphine. However, little is known on the rate of [[phosphate]]-[[phosphine]] transformation and its contribution to overall P cycling<ref name=”Gassman1994”> Gassman, G. (1994) Phosphine in the fluvial and marine hydrosphere, Marine Chemistry 45, 197–205.</ref> , <ref name="Tappin 2002"/> . <br />
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Tidal and marginal sediments are considered important sinks of N and P, although a quantitative estimation of their role remains uncertain<ref name=”Carpenter1997”> Carpenter, K. (1997) A critical appraisal of the methodology used in studies of material flux between [[saltmarshes]] and coastal waters. Biogeochemistry of Intertidal Sediments, T.D. Jickells, and J.E. Rae, Eds. (Cambridge University Press), pp. 59–83.</ref> ,. <ref name=”Ruddy1998a”> Ruddy, G., C. M. Turley, and T.E.R. Jones (1998a), Ecological interaction and sediment transport on an intertidal mudflat I. Evidence for a biologically mediated sediment-water interface. Sedimentary Processes in the Intertidal Zone, K.S. Black, D.M. Paterson, and A. Cramp, Eds. Geological Society of London Special Publications 139, pp. 135–148.</ref> ,. <ref name=”Ruddy1998b”> Ruddy, G., C.M. Turley, and T.E.R. Jones (1998b), Ecological interaction and sediment transport on an intertidal mudflat II. An experimental dynamic model of the sediment-water interface. Sedimentary Processes in the Intertidal Zone. K.S. Black, D.M. Paterson, and A. Cramp, Eds. Geological Society of London Special Publications 139, pp. 149–166.</ref> . On the global scale, it is generally accepted that intertidal sediments are more efficient for P burial than for N<ref name=”Billen1991”> Billen, G., C. Lancelot, and M. Meybeck (1991), N, P and Si retention along the aquatic continuum from land to ocean. Ocean Margin Processes in Global Change, R.F.C Mantoura, J.-M. Martin, and R. Wollast, Eds. (John Wiley & Sons Ltd.), pp. 19-44.</ref> <ref name=”Howarth1995”> Howarth, R., H. Jensen, R. Marino, and H. Postma, Phosphorus in the Global Environment:Transfers, Cycles and Management, H. Tiessen, Ed., Scientific Committee on Problems of the Environment 54. (Wiley, New York, 1995), pp. 323–356.</ref> .<br />
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===Silicon===<br />
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Relevant Si species in the aquatic environments include dissolved Si (DSi), mainly as undissociated monomeric silicic acid, Si(OH)<sub>4</sub>, and particulate Si (biogeneic [[silica]], BSiO<sub>2</sub>), which includes the amorphous silica in both living biomass and biogenic detritus in surface waters, soils and sediments. The main transformation processes are the uptake of DSi and the biomineralisation as BSiO2 in plants and organisms, as well as the dissolution of BSiO2 back to DSi. Over sufficiently long time scales, BSiO<sub>2</sub> may undergo significant chemical and mineralogical changes<ref name=”VanCappellan2002”> Van Cappellen, P., S. Dixit, and J. van Beusekom (2002), Biogenic silica dissolution in the oceans: Reconciling experimental and field-based dissolution rates, Global Biogeochemical Cycles 16, 1075, doi:10.1029/2001GB001431.</ref> , even including a complete diagenetic transformation of the opaline silica into alumino-silicate minerals. <ref name=”Michalopoulos2000”> Michalopoulos, P., R.C. Aller, and R.J. Reeder (2000), Conversion of diatoms to clays during early diagenesis in tropical, continental shelf muds, Geology 28, 1095-1098.</ref>.<br />
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The major producers of BSiO<sub<2</sub> in marine environments are diatoms. However, other organisms such as [[radiolarians]], [[sponges]] and [[chrysophytes]] may be important local sources of BSiO<sub>2</sub><ref name=”Simpson1981”> Simpspon, T.L. and B.E. Volcani (1981), Silicon and Siliceous Structures in Biological Systems, Springer-Verlag NY, 587 pp </ref> . Large quantities of DSi are also fixed on land by higher plants, forming amorphous silica deposits, known as [[phytoliths]]<ref name=”Piperno1998”> Piperno, D.L. (1998), Phytolith analysis. An archaeological and geological perspective. London: Academic Press.</ref> . Their role in the Si cycle has only recently been studied<ref name=”Bartoli1983”> Bartoli, F. (1983), The biogeochemical cycle of silicon in two temperate forest ecosystems, Ecological Bulletins (Stockholm) 35, 469–476.</ref> ,<ref name=”Meunier1999”> Meunier, J.D., F. Colin, and C. Alarcon (1999), Biogenic silica storage in soils, Geology 27, 835-838. </ref> . In general, riverine Si fluxes have been much less altered by human activity than those of N and P. However, increased damming of major rivers has promoted siliceous phytoplankton blooms<ref name=”Billen1991”> Billen, G., C. Lancelot, and M. Meybeck (1991), N, P and Si retention along the aquatic continuum from land to ocean.</ref> ,<ref name="Humborg1997"> Humborg, C., V. Ittekot, A. Cociosu, and B. v. Bdungen (1997), Effect of Danube River dam on Black Sea biogeochemistry and ecosystem structure, Nature 386, 385 – 388.</ref> , and therefore, reduced Si fluxes to the coastal zone. For example, the damming of the Danube has reduced the DSi concentration by more than 50%<ref name="Humborg1997"/>.<br />
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==See also==<br />
:[[European Context of Nutrient Dynamics]]<br />
:[[Eutrophication]]<br />
:[[Eutrophication in coastal environments]]<br />
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==External links==<br />
:[http://www.eloisegroup.org/themes/nutrients/contents.htm ELOISE Nutrient Dynamics in European Water Systems ONLINE]<br />
:[http://www.eloisegroup.org/themes/nutrients/pdf/nutrient_dynamics.pdf ELOISE Nutrient Dynamics in European Water Systems in pdf format]<br />
:[http://www.eloisegroup.org/themes/nutrients/casesintro.htm Case studies]<br />
:[http://www.loicz.org/ LOICZ Land-Ocean Interactions in the Coastal Zone]<br />
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==References==<br />
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[[Category:Coastal and marine ecosystems]] <br />
[[Category:Coastal and marine pollution]]<br />
[[Category:Eutrophication]]</div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Zooplankton&diff=76208Zooplankton2019-12-04T19:02:39Z<p>Dronkers J: </p>
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Definition|title=Zooplankton<br />
|definition= Microscopic planktonic animals that float freely in the open water. <ref>CoPraNet glossary [http://www.coastalpractice.net/glossary/index.htm]</ref>. <br />
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Different types of zooplankton: see [[Marine Plankton]].<br />
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==References==<br />
<references/></div>Dronkers Jhttp://www.coastalwiki.org/w/index.php?title=Phytoplankton&diff=76207Phytoplankton2019-12-04T18:59:04Z<p>Dronkers J: </p>
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Definition|title=Phytoplankton<br />
|definition= Microscopically small plants which float or swim weakly in fresh or salt water bodies. <br />
<ref>CoPraNet glossary [http://www.coastalpractice.net/glossary/index.htm]</ref>. <br />
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Different types of phytoplankton: see [[Marine Plankton]].<br />
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==References==<br />
<references/></div>Dronkers J