Difference between revisions of "Waves"

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==Waves==
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There is typically a distinction between short waves, which are waves with periods less than approximately 20 s, and long waves or long period oscillations, which are oscillations with periods between 20-30 s and 40 min. Water-level oscillations with periods or recurrence intervals larger than around 1 hour, such as [[tide|astronomical tide]] and [[storm surge]], are referred to as water-level variations. The short waves are wind waves and swell, whereas long waves are divided into [[surf beat]]s, [[harbor resonance]], [[seiche]] and [[tsunami]]s. Natural waves can be viewed as a wave field consisting of a large number of single wave components each characterised by a [[wave height]], a [[wave period]] and a propagation direction. Wave fields with many different [[wave period]]s and heights are called irregular.
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There is typically a distinction between short waves, which are waves with periods less than approximately 20 s, and long waves or long period oscillations, which are oscillations with periods between 20-30 s and 40 min. Water-level oscillations with periods or recurrence intervals larger than around 1 hour, such as astronomical tide and storm surge, are referred to as water-level variations. The short waves are wind waves and swell, whereas long waves are divided into surf-beats, harbour resonance, seiche and tsunamis.
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==Wave classifications==
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Sea waves can be classified in different ways, depending on the parameters considered <ref>Curto, D., Franzitta, V. and  Guercio, A. 2021. SeaWave Energy. A Review of the Current Technologies and Perspectives. Energies 14, 6604</ref>.
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Considering the parameter <math>r=h/L</math>, the ratio of water depth <math>h </math> and wavelength <math>L</math>, a commonly used classification is<ref>Cornett, A. 2008. A global wave energy resource assessment. In: Proceedings of the 18th International Offshore and Polar Engineering Conference, Vancouver, BC, Canada, 6–11 July 2008; ISOPE-2008-TPC-579, pp. 1–9</ref>:
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{|  style="border-collapse:collapse;background:ivory;" cellpadding=5px align=center width=100%
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|+ '''Table 1. Wave classification according to the ratio <math>r=h/L</math> of water depth <math>h </math> and wavelength <math>L</math>.'''
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|- style="font-size: 12px; text-align:center; border:2px solid lightblue"
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| width="25%" style="border:2px solid lightblue; background:ivory"| <math>r</math>
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! width="25% style="border:2px solid lightblue;"| < 0.05
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! width="25% style="border:2px solid lightblue;"| 0.05 – 0.5
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! width="25% style="border:2px solid lightblue;"| > 0.5
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|-
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| style="border:2px solid lightblue;text-align:center; background:ivory"| '''classification'''
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! style="border:2px solid lightblue;text-align:center" | shallow water or long wave
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! style="border:2px solid lightblue;text-align:center" | intermediate water wave
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! style="border:2px solid lightblue;text-align:center" | deep water or short wave
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|}
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Considering the wave period <math>T</math>, waves can be classified as in the table below<ref>Toffoli, A. and Bitner-Gregersen, E.M. 2017. Types of Ocean Surface Waves, Wave Classification. Encycl. Marit. Offshore Eng. 2017: 1–8</ref>:
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{|  style="border-collapse:collapse;background:ivory;" cellpadding=5px align=center width=100%
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|+ '''Table 2. Wave classification according to wave period <math>T</math>'''.
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|- style="font-size: 13px; text-align:center; background:lightblue"
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! width="10% style="border:2px solid lightblue;"| period
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! width="30% style="border:2px solid lightblue;"| wave type
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! width="60% style="border:2px solid lightblue;"| generation mechanism
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|- style="font-size: 12px; text-align:center; border:2px solid lightblue"
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! style="border:2px solid lightblue;"| <math>\boldsymbol{T < 0.1 s}</math>
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! style="border:2px solid lightblue;"| Capillary waves
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! style="border:2px solid lightblue;"| Generated by wind and restored by surface tension
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|- style="font-size: 12px"
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! style="border:2px solid lightblue;"| <math>\boldsymbol{0.1 < T <1 s}</math>
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! style="border:2px solid lightblue;"| Ultra-gravity waves (0.1 s < T < 1 s)
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! style="border:2px solid lightblue;"| Generated by wind and restored by surface tension and gravity
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|- style="font-size: 12px"
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! style= "border:2px solid lightblue;"| <math>\boldsymbol{1 < T < 30 s}</math>
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! style="border:2px solid lightblue;"| Gravity waves
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! style="border:2px solid lightblue;"| Generated by wind and restored by gravity
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|- style="font-size: 12px"
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! style="border:2px solid lightblue;"| <math>\boldsymbol{30 s < T < 5 min}</math>
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! style="border:2px solid lightblue;"| Infra-gravity waves
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! style="border:2px solid lightblue;"| Caused by wind and atmospheric pressure gradients and restored by gravity
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|- style="font-size: 12px"
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! style="border:2px solid lightblue;"| <math>\boldsymbol{5 min < T < 12 h}</math>
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! style="border:2px solid lightblue;"| Long-period waves (seiches, storm surges, tsunamis  
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! style="border:2px solid lightblue;"| Caused by atmospheric pressure gradients and earthquake and restored by gravity
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|- style="font-size: 12px"
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! style="border:2px solid lightblue;"| <math>\boldsymbol{12 h < T < 24 h}</math>
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! style="border:2px solid lightblue;"| Ordinary tidal waves
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! style="border:2px solid lightblue;"| Due to the gravitational attraction of celestial bodies (moon and sun) and restored by gravity and Coriolis force
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|- style="font-size: 12px"
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! style="border:2px solid lightblue;"| <math>\boldsymbol{T > 24 h}</math>
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! style="border:2px solid lightblue;"| Trans-tidal waves
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! style="border:2px solid lightblue;"| Due to storms and gravitational attraction and restored by gravity and Coriolis force
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|}
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In oceanography, the term “sea state” is used to indicate the temporary (about a half-hour) and local significant wave height <math>H_s</math> of the sea surface (with respect to wind waves and swell) as a consequence of wind interaction. The World Meteorological Organization (WMO) defines the sea states according to the Douglas Sea Scale of the table below:
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{|  style="border-collapse:collapse;background:ivory;" cellpadding=5px align=center width=100%
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|+ '''Table 3. Wave classification according to the Douglas Sea Scale.'''
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|- style="font-size: 12px; text-align:center; background:ivory"
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! width="10% style="border:2px solid lightblue;"| <math>\boldsymbol{H_s}</math> [m]
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! width="10% style="border:2px solid lightblue;"| < 0.1
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! width="10% style="border:2px solid lightblue;"| 0.1 – 0.5
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! width="10% style="border:2px solid lightblue;"| 0.5 – 1.25
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! width="10% style="border:2px solid lightblue;"| 1.25 – 2.5
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! width="10% style="border:2px solid lightblue;"| 2.5 - 4
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! width="10% style="border:2px solid lightblue;"| 4 - 6
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! width="10% style="border:2px solid lightblue;"| 6 - 9
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! width="10% style="border:2px solid lightblue;"| 9 – 14
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! width="10% style="border:2px solid lightblue;"| > 14
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|-
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! style="border:2px solid lightblue;"| classification
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! style="border:2px solid lightblue;"| calm (glassy)
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! style="border:2px solid lightblue;"| smooth (wavelets)
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! style="border:2px solid lightblue;"| slight
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! style="border:2px solid lightblue;"| moderate
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! style="border:2px solid lightblue;"| rough
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! style="border:2px solid lightblue;"| very rough
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! style="border:2px solid lightblue;"| high
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! style="border:2px solid lightblue;"| very high
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! style="border:2px solid lightblue;"| phenomenal
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|}
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==Short Waves==
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===Types of short waves===
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[[Image:irregular storm a.jpg|thumb|200px|Fig. 1a. Irregular directional storm waves (including white capping)]]
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[[Image:irregular storm b.jpg|thumb|200px|Fig. 1b. Regular unidirectional swell.]]
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<ref name="Aagard">Written by Aagard, Troels. 2007.</ref>Short waves are waves, generated by the wind that propagate towards the beach. They can be either actively forced by the wind (wind waves - see below) or they can have left their generation area (swell waves - see below). [[Incident wave|Incident waves]] are the primary source of energy input to the beach. On their way from [[deep water]] towards the shoreline they undergo refraction and shoaling processes. In deep water, incident waves are nearly sinusoidal; as they propagate into shallower water (shoaling), their celerity and [[wavelength]] decrease and as the total energy flux should remain constant (according to linear theory and neglecting bottom friction), the wave height must increase while the [[wavelength]] decreases. 
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<ref name="Aagard"/>As the waves propagate towards the shoreline, the wave shape becomes increasingly skewed with peaked wave crests and longer, rounded wave troughs, and wave orbital velocities become larger under crests than under troughs. This is a characteristic of fundamental importance to sediment transport, especially seaward of the wave breakpoint as there will be a tendency for the incident waves to push sediment towards the beach, see [[Shoreface profile]].  
  
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Natural waves can be viewed as a wave field consisting of a large number of single wave components each characterised by a wave height, a wave period and a propagation direction. Wave fields with many different wave periods and heights are called irregular, and wave fields with many wave directions are called directional. A wave field can be more or less irregular and more or less directional.
 
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===Short Waves===
 
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====Types of waves====
 
 
The short waves are the single most important parameter in coastal morphology. Wave conditions vary considerably from site to site, depending mainly on the wind climate and on the type of water area. The short waves are divided into:
 
The short waves are the single most important parameter in coastal morphology. Wave conditions vary considerably from site to site, depending mainly on the wind climate and on the type of water area. The short waves are divided into:
  
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*Wind waves, also called storm waves, or sea. These are waves generated and influenced by the local wind field. Wind waves are normally relatively steep (high and short) and are often both irregular and directional, for which reason it is difficult to distinguish defined wave fronts. The waves are also referred to as short-crested. Wind waves tend to be destructive for the coastal profile because they generate an offshore (as opposed to onshore) movement of sediments, which results in a generally flat shoreface and a steep foreshore.
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*'''Wind waves''', also called storm waves, or sea. These are waves generated and influenced by the local wind field. Wind waves are normally relatively steep (high and short) and are often both irregular and directional, for which reason it is difficult to distinguish defined wave fronts. The waves are also referred to as short-crested. Wind waves tend to be destructive for the coastal profile because they generate an offshore (as opposed to onshore) movement of sediments, which results in a generally flat shoreface and a steep foreshore.
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*Swell are waves, which have been generated by wind fields far away and have travelled long distances over deep water away from the wind field, which generated the waves. Their direction of propagation is thus not necessarily the same as the local wind direction. Swell waves are often relatively long, of moderate height, regular and unidirectional. Swell waves tend to build up the coastal profile to a steep shoreface.
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*'''Swell''' are waves, which have been generated by wind fields far away and have travelled long distances over deep water away from the wind field, which generated the waves. Their direction of propagation is thus not necessarily the same as the local wind direction. Swell waves are often relatively long, of moderate height, regular and unidirectional. Swell waves tend to build up the coastal profile to a steep shoreface.
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====Wave breaking====
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<ref name="Aagard"/>Depth-limited wave breaking is the prerequisite for the generation of [[nearshore]] currents and secondary wave phenomena. Seaward of the surf zone, any wave energy losses primarily occur through whitecapping and friction against the sea bed. As the waves approach the beach, however, depth-limited breaking will occur when orbital velocities, increasing towards the beach exceed the wave phase speed which decreases in the landward direction. The breaking wave height, <math>H_b</math> is related to the water depth at breaking, <math>h_b</math>, through
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<math>H_b = \gamma \, h_b ,</math>
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where <math>\gamma</math> is the [[breaker index]]. In nature waves are irregular and random and using <math>H_{rms}</math> as the measure of wave height, the maximum time-averaged value of the breaker index (<math><\gamma_{rms}></math>) is in the range 0.35-0.8 , see [[Breaker index]].
  
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[[Image:irregular storm.jpg|thumb]]
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The predominant type of wave breaking depends on wave steepness and beach slope expressed through the surf scaling parameter:
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[[Image:irregular storm.jpg|thumb|Irregular directional storm waves (including white capping) and regular unidirectional swell.]]
 
  
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Fig 5.1
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<math>\epsilon = \pi H / T g \tan^2 \beta , </math>
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Irregular directional storm waves (including white-capping) and regular unidirectional swell.
 
  
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====Wave generation====
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where <math>T</math> is wave period, <math>g</math> is the acceleration of gravity and <math>\tan \beta</math> is the beach slope. With spilling breakers, <math>\epsilon > 20</math>, plunging occurs for <math>2.5 <\epsilon < 20</math> and surging breakers predominate when <math>\epsilon < 2.5</math>.
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As waves propagate towards the beach, short wave energy is gradually lost through breaking and long [[infragravity waves]] become more important.
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For a more detailed introduction the reader is referred to the article [[Shallow-water wave theory]].
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===Wave generation===
 
Wind waves are generated as a result of the action of the wind on the surface of the water. The wave height, wave period, propagation direction and duration of the wave field at a certain location depend on:
 
Wind waves are generated as a result of the action of the wind on the surface of the water. The wave height, wave period, propagation direction and duration of the wave field at a certain location depend on:
  
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*The wind field (speed, direction and duration)
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#The wind field (speed, direction and duration)
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*The fetch of the wind field (meteorological fetch) or the water area (geographical fetch)
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#The fetch of the wind field (meteorological fetch) or the water area (geographical fetch)
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*The water depth over the wave generation area.
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#The water depth over the wave generation area.
  
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Swell is, as previously stated, wind waves generated elsewhere but transformed as they propagate away from the generation area. The dissipation processes, such as wave-breaking, attenuate the short period much more than the long period components. This process acts as a filter, whereby the resulting long-crested swell will consist of relatively long waves with moderate wave height.
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Swell is, as previously stated, wind waves generated elsewhere but transformed as they propagate away from the generation area. The dissipation processes, such as wave-breaking, attenuate the short period much more than the long period components. This process acts as a filter, whereby the resulting long-crested swell will consist of relatively long ([[wavelength]]) waves with moderate wave height.
  
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====[[Wave transformation]]====
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===[[Wave transformation]]===
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The types of transformation discussed here are mainly related to wave phenomena occurring in the natural environment. When the waves approach the shoreline, they are affected by the seabed through processes such as refraction, shoaling, bottom friction and wave breaking. However, wave breaking also occurs in deep water when the waves are too steep. If the waves meet major structures or abrupt changes in the coastline, they will be transformed by diffraction. If waves meet a submerged reef or structure, they will overtop the reef – see [[Wave transformation]].
  
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====[[Statistical description of wave parameters]]====
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===[[Statistical description of wave parameters]]===
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Because of the random nature of natural waves, a statistical description of the waves is normally always used. The individual 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 in this section – see [[Statistical description of wave parameters]].
  
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====Wave climate classification according to wind climate====
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===Wave climate classification according to wind climate===
 
The different wind climates, which dominate different oceans and regions, cause correspondingly characteristic wave climates. These characteristic wave climates can be classified as follows:
 
The different wind climates, which dominate different oceans and regions, cause correspondingly characteristic wave climates. These characteristic wave climates can be classified as follows:
 
*Storm wave climate.  
 
*Storm wave climate.  
Line 38: Line 148:
 
*Tropical cyclone climate.  
 
*Tropical cyclone climate.  
  
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For details on these calssifications follow the link [[Wave climate classification according to wind climate]].
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For details on these classifications follow the link [[Wave climate classification according to wind climate]].
  
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===Long Waves===
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==Long Waves==
 
The long waves are primarily second order phenomena of shallow water wave processes. The four main types of long waves are described in the following.
 
The long waves are primarily second order phenomena of shallow water wave processes. The four main types of long waves are described in the following.
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====Surf beat====
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===Surf beat===
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Natural waves often show a tendency to wave grouping, where a series of high waves follows a series of low waves. This is especially pronounced on open sea-coasts, where the incoming waves may be of different origins and will thus have a large spreading in wave heights, wave directions, and wave periods (or frequencies). Wave grouping will cause oscillations in the wave set-up with a period corresponding to approx. 6 – 8 times the mean wave period; this phenomenon is called surf-beats. Surf-beats near port entrances are very important in relation to mooring conditions in the port basins and sedimentation in the port entrance.
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[[image:wave set up_a.jpg|thumb|300px|Fig. 2. Wave set-up]]
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Natural waves often show a tendency to wave grouping, where a series of high waves follows a series of low waves. This is especially pronounced on open sea-coasts, where the incoming waves may be of different origins and will thus have a large spreading in wave heights, wave directions, and wave periods (or frequencies). Wave grouping will cause oscillations in the [[wave set-up]] with a period corresponding to approx. 6 – 8 times the mean wave period; this phenomenon is called surf-beats (sea also [[Infragravity waves]]). Surf-beats near port entrances are very important in relation to mooring conditions in the port basins and sedimentation in the port entrance.
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<br style="clear:both;"/>
  
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===Harbour resonance===
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[[image:wave set up_b.jpg|thumb|Fig. 3. Surf beat generated harbour resonance, recorded by a tide gauge]]
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Harbour resonance is the forced resonant oscillation of a semi-confined water body (e.g. a harbour basin or a lagoon) connected to a larger water body (the sea). If long-period oscillations are present in the sea, e.g. due to [[seiche]]s, large oscillations at the natural frequency of the semi-confined water body may occur. Oscillations at the first harmonic, which are the simplest mode of resonance, are often called the pumping or Helmholz mode. See also [[Infragravity waves#Seiche in harbors|harbour seiches induced by infragravity waves]].
  
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Harbour resonance normally has periods in the range of 2 to 10 minutes. It is especially important in connection with the mooring conditions of large vessels, as their resonance period for the so-called surge motion is often close to that of the harbour resonance. In addition, the associated water exchange may cause siltation. It is important to establish whether seiches do occur in an area through field investigations, and if so, to take it into account in the layout of the port. If seiches do occur, they will inevitably penetrate the entrance. However, the impact on the port may be minimised through a proper layout.
  
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[[image:wave set up_c.jpg|thumb|right|Fig. 4. Circulation caused by the gradient in the wave set-up]]
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===Lake seiche===
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A lake seiche is the free oscillation of a water body, caused by rapid variations in the wind conditions. Seiches can occur in closed water areas, such as lakes or lagoons, and in semi-closed water bodies, such as bays. The period of the seiche oscillation is typically in the range of 2 to 40 minutes.
  
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Fig 5.10
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===[[Tsunami]]===
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[[image:wave set up_a.jpg|thumb]]
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<!--Threats to the coastal zone, Section 6 links here -->
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[[image:wave set up_b.jpg|thumb]]
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Tsunamis are long waves caused by a strong local disturbance of the water mass, for example by seismic events. Tsunamis generally consist of a few successive waves with wavelengths typically much larger than the wavelength of wind-generated waves and much smaller than the wavelength of tidal waves. Tsunamis travel very fast in the deep oceans. If the water depth is 5000 m, the speed will be more than 200 m/s or about 800 km/hour. A tsunami is normally not very high in deep water, but when it approaches the coastline, the wave will be shoaling and can reach a height of more than 10 m. Tsunamis are rare and coastal projects seldom take them into account. However, in very sensitive projects, such as nuclear power plants located in the coastal hinterland, the risk must be considered. For further details see the article [[Tsunami]].
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[[image:wave set up_c.jpg|thumb|Wave set-up (upper), surf beat generated harbour resonance, recorded by a tide gauge, in a small port (middle) and circulation caused by the gradient in the wave set-up. ]]
 
  
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==<ref name="Aagard"/>Infragravity waves==
  
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[[Image:infragravity.jpg|thumb|Fig. 5. Infragravity wave orbital velocities at two Danish beaches, plotted as a function of relative water depth. <math>h/h_b = 0</math> is at the [[shoreline]], and <math>h/h_b = 1</math> indicates the mean position of the wave breakpoint.]]
  
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Wave set-up (upper), surf beat generated harbour resonance, recorded by a tide gauge, in a small port (middle) and circulation caused by the gradient in the wave set-up.
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[[Infragravity waves]] are waves that are forced by difference interactions in the incident wave frequency band and consequently they have frequencies which are lower than the frequencies of incident waves ~0.005-0.05 Hz. From a morphodynamic viewpoint, much of the interest in infragravity waves is due to the fact that they are often standing in the cross-shore direction and sometimes also alongshore, therefore resulting in a stationary drift velocity field in the bottom boundary layer. They can therefore potentially provide a mechanism for [[nearshore]] bar formation and the generation of three-dimensional features such as rip currents and rhythmic bars. Apart from quasi-steady drift velocities in the boundary layer, orbital velocities associated with these motions can generate oscillatory sediment fluxes which have been demonstrated to be important to the net sediment transport in the surf zone.  
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====Harbour resonance====
 
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Harbour resonance is forced oscillation of a confined water body (e.g. a harbour basin or a lagoon) connected to a larger water body (the sea). If long-period oscillations are present in the sea, e.g. due to wave grouping or surf-beats or seiche, large oscillations at the natural frequency of the confined water body may occur. Oscillations at the first harmonic, which are the simplest mode of resonance, are often called the pumping or Helmholz mode.  
 
  
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Harbour resonance normally has periods in the range of 2 to 10 minutes. It is especially important in connection with the mooring conditions for large vessels, as their resonance period for the so-called surge motion is often close to that of the harbour resonance. In addition the associated water exchange may cause siltation.
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Nearshore-standing infragravity waves may occur as either leaky mode waves which are two-dimensional standing waves having a succession of antinodes and nodes away from the point of reflection (e.g. the shoreline), or as edge waves which are three-dimensional waves trapped against the [[nearshore]] by reflection and refraction and which can propagate alongshore (progressive edge waves) or be longshore-standing (standing edge waves). Edge waves have a finite number of nodes/antinodes in the cross-shore direction (the number of cross-shore surface elevation nodes is called the mode number, <math>n</math>), and a theoretically infinite number of nodes/antinodes in the longshore dimension.  
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====Seiche====
 
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A seiche is the free oscillation of a water body, probably caused by rapid variations in the wind conditions. Seiche can occur in closed water areas, such as lakes or lagoons, and in semi-closed water bodies, such as bays. The period of the seiche oscillation is typically in the range of 2 to 40 minutes. Seiche can influence a port in the same manner as surf-beats. It is important to establish whether seiche is present in an area through field investigations, and if so, to take it into account in the layout of the port. Surf-beat influence within a port is often caused by an inexpedient layout. The influence of surf-beat is not applicable for seiche, as seiche is not limited to the nearshore zone. This means that if seiche motion is present in an area, it will inevitably penetrate the entrance. However, its impact on the port may be minimised through a proper layout.
 
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====Tsunami====
 
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A tsunami is a single wave, which is generated by sub-sea earthquakes; it typically has a period of 5 to 60 minutes. Tsunami waves can travel long distances across the oceans; they are similar to shallow water waves, which means that the speed v is calculated as the square root of the product of the water depth and the acceleration of gravity, v = (gh)<sup>1/2</sup>. Consequently, tsunamis travel very fast in the deep oceans. If the water depth is 5000 m, the speed will be more than 200 m/s or about 800 km/hour. A tsunami is normally not very high in deep water, but when it approaches the coastline, the wave will be shoaling and can reach a height of more than 10 m. Tsunamis are rare and coastal projects seldom take them into account. However, in very sensitive projects, such as nuclear power plants located in the coastal hinterland, the risk must be considered.
 
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==Currents==
 
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The various types of currents in the sea, which may be important to coastal processes in one way or another, are described in the following.
 
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===Currents in the Open Sea===
 
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Tidal currents are formed by the gravitational forces of the sun, the moon and the planets. These currents are of oscillatory nature with typical periods of around 12 or 24 hours, the so-called semi-diurnal and diurnal tidal currents. The tidal currents are strongest in large water depths away from the coastline and in straits where the current is forced into a narrow area. The most important tidal currents in relation to coastal morphology are the currents generated in tidal inlets. Typical maximum current speeds in tidal inlets are approx. 1 m/s, whereas tidal current speeds in straits and estuaries can reach speeds as high as approx. 3 m/s.
 
 
   
 
   
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Fig 5.11
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Infragravity wave heights and orbital velocities increase towards the shoreline (see Fig. 5. below), while incident wave heights decrease landward due to wave breaking. Infragravity waves should therefore be of increasing relative importance with proximity to the shoreline and sediment resuspension and transport become increasingly affected by infragravity motions. A more comprehensive treatment of [[nearshore]] infragravity waves can be found in e.g. Aagaard and Masselink (1999)<ref>Aagaard, T. and Masselink, G., 1999. The Surf Zone. In: A.D.Short (ed) Handbook of Beach and Shoreface Morphodynamics, Wiley Interscience, pp.72-118.</ref> and [[Infragravity waves]].
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[[image:tidal currents.jpg|thumb|Tidal currents in tidal inlet (Caravelas in Brazil).]]
 
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Tidal currents in tidal inlet (Caravelas in Brazil).
 
  
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Wind-generated currents are caused by the direct action of the wind shear stress on the surface of the water. The wind-generated currents are normally located in the upper layer of the water body and are therefore not very important from a morphological point of view. In very shallow coastal waters and lagoons, the wind-generated current can, however, be of some importance. Wind-generated current speeds are typically less than 5 per cent of the wind speed.
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==Measurement of Waves==
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Waves are traditionally measured with wave rider buoys. More recently, remote sensing techniques for measuring waves have been developed, see [[Waves and currents by X-band radar | Measuring waves and currents by X-band radar]].
  
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Storm surge current is the current generated by the total effect of the wind shear stress and the barometric pressure gradients over the entire area of water affected by a specific storm. This type of current is similar to the tidal currents. The horizontal current velocity follows a logarithmic distribution in the water profile and has the same characteristics as the tidal current. It is strongest at large water depths away from the coastline and in confined areas, such as straits and tidal inlets.
 
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===Current in the Nearshore Zone.===
 
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====Shore-parallel currents====
 
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The longshore current is the dominant current in the nearshore zone. The longshore current is generated by the shore-parallel component of the stresses associated with the breaking process for obliquely incoming waves, the so-called radiation stresses, and by the surplus water which is carried across the breaker-zone towards the coastline. This current has its maximum close to the breaker-line. During storms the longshore current can reach speeds exceeding 2.5 m/s. The longshore current carries sediment along the shoreline, the so-called littoral drift; this mechanism will be discussed further in Section 6.
 
  
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The longshore current is generally parallel to the coastline and it varies in strength approximately proportional to the square root of the wave height and with sin2b, where b is the wave incidence angle at breaking. As the position of the breaking line constantly shifts due to the irregularity of natural wave fields and since the distance to the breaker-line varies with the wave height, the distribution of the longshore current in the coastal profile will vary accordingly.
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==Related articles==
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====Shore-normal currents====
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:[[Shallow-water wave theory]]
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Rip currents
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:[[Statistical description of wave parameters]]
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At certain intervals along the coastline, the longshore current will form a rip current. It is a local current directed away from the shore, bringing the surplus water carried over the bars in the breaking process back into deep water. The rip opening in the bars will often form the lowest section of the coastal profile; a local setback in the shoreline is often seen opposite the rip opening. The rip opening travels slowly downstream.
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:[[Infragravity waves]]
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:[[Tsunami]]
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:[[Seiche]]
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:[[Wave set-up]]
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:[[Wave transformation]]
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:[[Breaker index]]
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:[[Swash zone dynamics]]
  
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Fig 5.12
 
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[[image:longshore distribution.jpg|thumb|Distribution in longshore current in a coastal profile and rip current pattern.]]
 
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Distribution in longshore current in a coastal profile and rip current pattern.
 
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Cross-currents along the shore-normal coastal profile
 
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Cross-currents occur especially in the surf-zone. Three contributions balance each other:
 
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*Mass transport, or wave drift, is a phenomenon occurring during wave motion over both sloping and horizontal beds. Water particles near the surface will be transported in the direction of wave propagation when waves travel over an area. This phenomenon is called the mass transport. In the surf-zone the mass transport is directed towards the coast.
 
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*Surface roller drift. When the waves break, water is transported in the surface rollers towards the coast. This is the so-called surface roller drift.
 
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*Undertow. In the surf-zone, the above two contributions are concentrated near the surface. As the net flow is zero, they are compensated for by a return flow in the offshore direction, which is concentrated near the bed. This is the so-called undertow. The undertow is important in the formation of bars.
 
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====Two-dimensional currents in the nearshore zone====
 
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Along a straight shoreline, the above-mentioned shore-parallel and shore-normal current patterns dominate. The currents discussed in this sub-chapter are two-dimensional in the horizontal plane due to complex bathymetries and structures in the nearshore zone.
 
  
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Two-dimensional current patterns occur, especially in the following situations:
 
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*When the bathymetry is irregular and very different from the smooth shore-parallel pattern of depth contours characteristic of sandy shorelines, and also when the coastline is very irregular. This can, for example, be at partially rocky coastlines or along coastlines where coral reefs or other hard reefs are present. Irregular depth contours give rise to irregular wave patterns, which again can cause special current phenomena important to the understanding of the coastal morphology. Irregular bathymetry combined with an irregular coastline adds further to the complexity of the wave and current pattern. Reefs provide partial protection against wave action. However, they also generate overtopping of water and compensation currents behind the reef. At low sections of the reef or in gaps in the reef, the surplus water returns to the sea in rip-like jets. This is the pattern for both submerged reefs and emerged reefs with overtopping during storms. Such current systems are of great importance to the morphology behind the reef. Changes in reef structure, natural or man-made, can cause great changes in the morphology. 
 
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*In the vicinity of coastal structures, such as groynes, coastal breakwaters and port structures. Such structures influence the current pattern in two principally different ways: by obstructing the shore-parallel current and by setting up secondary circulation currents.
 
  
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The nature of the obstruction of the shore-parallel currents of course depends on the extension and shape of the coastal structure. If the structure is located within the breaker-zone, the obstruction leads to offshore-directed jet-like currents, which cause loss of beach material. If the structure is a port, the current will follow the upstream breakwater and finally reach the entrance area. The currents in the entrance area will both influence the navigation conditions and cause sedimentation, consequently the design of the entrance is important. It must provide a smooth and predictable current pattern so its impact on navigation is acceptable, sedimentation must be minimised and the bypass of sand must be optimised. The answer is a smooth layout of the main and secondary breakwaters combined with a narrow entrance pointing towards the prevailing waves.
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==References==
 +
<references/>
  
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At the leeward side of coastal structures, special current patterns caused by the sheltering effect of the structure in the diffraction area can develop. Sheltered or partly sheltered areas may result in circulation currents along the inner shoreface as well as return currents leading to deep water. The reason for this is that the wave set-up in the sheltered areas is smaller than in the adjacent exposed areas and this generates a gradient in the water-level towards the sheltered areas. These circulation currents in the sheltered areas can be dangerous for swimmers who are using the sheltered area for swimming during rough weather. Another problem is that the sheltered areas will be exposed to sedimentation and such areas must, therefore, be avoided when planning small ports.  
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==Further reading==
 +
Mangor, K., Drønen, N. K., Kaergaard, K.H. and Kristensen, N.E. 2017. Shoreline management guidelines. DHI https://www.dhigroup.com/marine-water/ebook-shoreline-management-guidelines.
  
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Fig 5.13
 
  
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[[image:lee circulation_a.jpg|thumb|Lee circulation patterns for a coastal breakwater and a small port. The optimal shape of a small port, avoiding the lee area.]]
 
  
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[[image:lee circulation_b.jpg|thumb|Lee circulation patterns for a coastal breakwater and a small port. The optimal shape of a small port, avoiding the lee area.]]
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{{author
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Lee circulation patterns for a coastal breakwater and a small port. The optimal shape of a small port, avoiding the lee area.
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|AuthorID=13331
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|AuthorFullName=Mangor, Karsten
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If the structure extends beyond the breaker-zone, the shore-parallel current will be directed along the structure, where the increasing depth will decrease the speed. The current will deposit the sand in a shoal off the breaker-zone upstream of the structure. In the case of a major port, the longshore current will not reach the entrance area. In the lee area of a major coastal structure, the effect of return currents towards the sheltered area will also be pronounced, but the current circulation pattern will be smoother and less dangerous for swimmers. The sheltered areas will act as a sedimentation area adding severely to effects of the lee side erosion outside the sheltered area of such structures. Once again, sheltered areas should be avoided.
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|AuthorName=Karsten}}
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*Adjacent to special morphological features such as sand spits, river mouths and tidal inlets. The current patterns and the associated sediment transport at such locations can be very complicated. Only a few general comments will be given in this overview of currents and their impacts.
 
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In tidal inlets and river mouths there are often concentrated currents in the gorge section of the mouth, but seawards of this area the current pattern expands and the current speed decreases. This is also the case landwards of the gorge section in tidal inlets. The gorge section is often deep and narrow, whereas the expanding currents on either side tend to form the ebb and flood shoals respectively. The ebb shoal tends to form a dome-shaped bar on littoral transport shorelines, on which the littoral transport bypasses the mouth/inlet.
 
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Fig 5.14
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[[Category:Physical coastal and marine processes]]
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[[image:ebb and flood.jpg|thumb|Ebb and flood shoals at tidal channel, Cay Calker, Belize. This area is mainly exposed to the tidal currents, whereas the wave climate is very mild.]]
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[[Category:Beaches]]
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Ebb and flood shoals at tidal channel, Cay Calker, Belize. This area is mainly exposed to the tidal currents, whereas the wave climate is very mild.
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[[Category:Hydrodynamics]]

Latest revision as of 16:09, 14 February 2024

There is typically a distinction between short waves, which are waves with periods less than approximately 20 s, and long waves or long period oscillations, which are oscillations with periods between 20-30 s and 40 min. Water-level oscillations with periods or recurrence intervals larger than around 1 hour, such as astronomical tide and storm surge, are referred to as water-level variations. The short waves are wind waves and swell, whereas long waves are divided into surf beats, harbor resonance, seiche and tsunamis. Natural waves can be viewed as a wave field consisting of a large number of single wave components each characterised by a wave height, a wave period and a propagation direction. Wave fields with many different wave periods and heights are called irregular.

Wave classifications

Sea waves can be classified in different ways, depending on the parameters considered [1]. Considering the parameter [math]r=h/L[/math], the ratio of water depth [math]h [/math] and wavelength [math]L[/math], a commonly used classification is[2]:


Table 1. Wave classification according to the ratio [math]r=h/L[/math] of water depth [math]h [/math] and wavelength [math]L[/math].
[math]r[/math] < 0.05 0.05 – 0.5 > 0.5
classification shallow water or long wave intermediate water wave deep water or short wave


Considering the wave period [math]T[/math], waves can be classified as in the table below[3]:


Table 2. Wave classification according to wave period [math]T[/math].
period wave type generation mechanism
[math]\boldsymbol{T \lt 0.1 s}[/math] Capillary waves Generated by wind and restored by surface tension
[math]\boldsymbol{0.1 \lt T \lt 1 s}[/math] Ultra-gravity waves (0.1 s < T < 1 s) Generated by wind and restored by surface tension and gravity
[math]\boldsymbol{1 \lt T \lt 30 s}[/math] Gravity waves Generated by wind and restored by gravity
[math]\boldsymbol{30 s \lt T \lt 5 min}[/math] Infra-gravity waves Caused by wind and atmospheric pressure gradients and restored by gravity
[math]\boldsymbol{5 min \lt T \lt 12 h}[/math] Long-period waves (seiches, storm surges, tsunamis Caused by atmospheric pressure gradients and earthquake and restored by gravity
[math]\boldsymbol{12 h \lt T \lt 24 h}[/math] Ordinary tidal waves Due to the gravitational attraction of celestial bodies (moon and sun) and restored by gravity and Coriolis force
[math]\boldsymbol{T \gt 24 h}[/math] Trans-tidal waves Due to storms and gravitational attraction and restored by gravity and Coriolis force


In oceanography, the term “sea state” is used to indicate the temporary (about a half-hour) and local significant wave height [math]H_s[/math] of the sea surface (with respect to wind waves and swell) as a consequence of wind interaction. The World Meteorological Organization (WMO) defines the sea states according to the Douglas Sea Scale of the table below:


Table 3. Wave classification according to the Douglas Sea Scale.
[math]\boldsymbol{H_s}[/math] [m] < 0.1 0.1 – 0.5 0.5 – 1.25 1.25 – 2.5 2.5 - 4 4 - 6 6 - 9 9 – 14 > 14
classification calm (glassy) smooth (wavelets) slight moderate rough very rough high very high phenomenal


Short Waves

Types of short waves

Fig. 1a. Irregular directional storm waves (including white capping)
Fig. 1b. Regular unidirectional swell.

[4]Short waves are waves, generated by the wind that propagate towards the beach. They can be either actively forced by the wind (wind waves - see below) or they can have left their generation area (swell waves - see below). Incident waves are the primary source of energy input to the beach. On their way from deep water towards the shoreline they undergo refraction and shoaling processes. In deep water, incident waves are nearly sinusoidal; as they propagate into shallower water (shoaling), their celerity and wavelength decrease and as the total energy flux should remain constant (according to linear theory and neglecting bottom friction), the wave height must increase while the wavelength decreases.

[4]As the waves propagate towards the shoreline, the wave shape becomes increasingly skewed with peaked wave crests and longer, rounded wave troughs, and wave orbital velocities become larger under crests than under troughs. This is a characteristic of fundamental importance to sediment transport, especially seaward of the wave breakpoint as there will be a tendency for the incident waves to push sediment towards the beach, see Shoreface profile.

The short waves are the single most important parameter in coastal morphology. Wave conditions vary considerably from site to site, depending mainly on the wind climate and on the type of water area. The short waves are divided into:

  • Wind waves, also called storm waves, or sea. These are waves generated and influenced by the local wind field. Wind waves are normally relatively steep (high and short) and are often both irregular and directional, for which reason it is difficult to distinguish defined wave fronts. The waves are also referred to as short-crested. Wind waves tend to be destructive for the coastal profile because they generate an offshore (as opposed to onshore) movement of sediments, which results in a generally flat shoreface and a steep foreshore.
  • Swell are waves, which have been generated by wind fields far away and have travelled long distances over deep water away from the wind field, which generated the waves. Their direction of propagation is thus not necessarily the same as the local wind direction. Swell waves are often relatively long, of moderate height, regular and unidirectional. Swell waves tend to build up the coastal profile to a steep shoreface.


Wave breaking

[4]Depth-limited wave breaking is the prerequisite for the generation of nearshore currents and secondary wave phenomena. Seaward of the surf zone, any wave energy losses primarily occur through whitecapping and friction against the sea bed. As the waves approach the beach, however, depth-limited breaking will occur when orbital velocities, increasing towards the beach exceed the wave phase speed which decreases in the landward direction. The breaking wave height, [math]H_b[/math] is related to the water depth at breaking, [math]h_b[/math], through

[math]H_b = \gamma \, h_b ,[/math]

where [math]\gamma[/math] is the breaker index. In nature waves are irregular and random and using [math]H_{rms}[/math] as the measure of wave height, the maximum time-averaged value of the breaker index ([math]\lt \gamma_{rms}\gt [/math]) is in the range 0.35-0.8 , see Breaker index.

The predominant type of wave breaking depends on wave steepness and beach slope expressed through the surf scaling parameter:

[math]\epsilon = \pi H / T g \tan^2 \beta , [/math]

where [math]T[/math] is wave period, [math]g[/math] is the acceleration of gravity and [math]\tan \beta[/math] is the beach slope. With spilling breakers, [math]\epsilon \gt 20[/math], plunging occurs for [math]2.5 \lt \epsilon \lt 20[/math] and surging breakers predominate when [math]\epsilon \lt 2.5[/math].

As waves propagate towards the beach, short wave energy is gradually lost through breaking and long infragravity waves become more important.

For a more detailed introduction the reader is referred to the article Shallow-water wave theory.

Wave generation

Wind waves are generated as a result of the action of the wind on the surface of the water. The wave height, wave period, propagation direction and duration of the wave field at a certain location depend on:

  1. The wind field (speed, direction and duration)
  2. The fetch of the wind field (meteorological fetch) or the water area (geographical fetch)
  3. The water depth over the wave generation area.

Swell is, as previously stated, wind waves generated elsewhere but transformed as they propagate away from the generation area. The dissipation processes, such as wave-breaking, attenuate the short period much more than the long period components. This process acts as a filter, whereby the resulting long-crested swell will consist of relatively long (wavelength) waves with moderate wave height.

Wave transformation

The types of transformation discussed here are mainly related to wave phenomena occurring in the natural environment. When the waves approach the shoreline, they are affected by the seabed through processes such as refraction, shoaling, bottom friction and wave breaking. However, wave breaking also occurs in deep water when the waves are too steep. If the waves meet major structures or abrupt changes in the coastline, they will be transformed by diffraction. If waves meet a submerged reef or structure, they will overtop the reef – see Wave transformation.

Statistical description of wave parameters

Because of the random nature of natural waves, a statistical description of the waves is normally always used. The individual 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 in this section – see Statistical description of wave parameters.

Wave climate classification according to wind climate

The different wind climates, which dominate different oceans and regions, cause correspondingly characteristic wave climates. These characteristic wave climates can be classified as follows:

  • Storm wave climate.
  • Swell climate.
  • Monsoon wave climate.
  • Tropical cyclone climate.

For details on these classifications follow the link Wave climate classification according to wind climate.

Long Waves

The long waves are primarily second order phenomena of shallow water wave processes. The four main types of long waves are described in the following.

Surf beat

Fig. 2. Wave set-up

Natural waves often show a tendency to wave grouping, where a series of high waves follows a series of low waves. This is especially pronounced on open sea-coasts, where the incoming waves may be of different origins and will thus have a large spreading in wave heights, wave directions, and wave periods (or frequencies). Wave grouping will cause oscillations in the wave set-up with a period corresponding to approx. 6 – 8 times the mean wave period; this phenomenon is called surf-beats (sea also Infragravity waves). Surf-beats near port entrances are very important in relation to mooring conditions in the port basins and sedimentation in the port entrance.

Harbour resonance

Fig. 3. Surf beat generated harbour resonance, recorded by a tide gauge

Harbour resonance is the forced resonant oscillation of a semi-confined water body (e.g. a harbour basin or a lagoon) connected to a larger water body (the sea). If long-period oscillations are present in the sea, e.g. due to seiches, large oscillations at the natural frequency of the semi-confined water body may occur. Oscillations at the first harmonic, which are the simplest mode of resonance, are often called the pumping or Helmholz mode. See also harbour seiches induced by infragravity waves.

Harbour resonance normally has periods in the range of 2 to 10 minutes. It is especially important in connection with the mooring conditions of large vessels, as their resonance period for the so-called surge motion is often close to that of the harbour resonance. In addition, the associated water exchange may cause siltation. It is important to establish whether seiches do occur in an area through field investigations, and if so, to take it into account in the layout of the port. If seiches do occur, they will inevitably penetrate the entrance. However, the impact on the port may be minimised through a proper layout.

Fig. 4. Circulation caused by the gradient in the wave set-up

Lake seiche

A lake seiche is the free oscillation of a water body, caused by rapid variations in the wind conditions. Seiches can occur in closed water areas, such as lakes or lagoons, and in semi-closed water bodies, such as bays. The period of the seiche oscillation is typically in the range of 2 to 40 minutes.

Tsunami

Tsunamis are long waves caused by a strong local disturbance of the water mass, for example by seismic events. Tsunamis generally consist of a few successive waves with wavelengths typically much larger than the wavelength of wind-generated waves and much smaller than the wavelength of tidal waves. Tsunamis travel very fast in the deep oceans. If the water depth is 5000 m, the speed will be more than 200 m/s or about 800 km/hour. A tsunami is normally not very high in deep water, but when it approaches the coastline, the wave will be shoaling and can reach a height of more than 10 m. Tsunamis are rare and coastal projects seldom take them into account. However, in very sensitive projects, such as nuclear power plants located in the coastal hinterland, the risk must be considered. For further details see the article Tsunami.

[4]Infragravity waves

Fig. 5. Infragravity wave orbital velocities at two Danish beaches, plotted as a function of relative water depth. [math]h/h_b = 0[/math] is at the shoreline, and [math]h/h_b = 1[/math] indicates the mean position of the wave breakpoint.

Infragravity waves are waves that are forced by difference interactions in the incident wave frequency band and consequently they have frequencies which are lower than the frequencies of incident waves ~0.005-0.05 Hz. From a morphodynamic viewpoint, much of the interest in infragravity waves is due to the fact that they are often standing in the cross-shore direction and sometimes also alongshore, therefore resulting in a stationary drift velocity field in the bottom boundary layer. They can therefore potentially provide a mechanism for nearshore bar formation and the generation of three-dimensional features such as rip currents and rhythmic bars. Apart from quasi-steady drift velocities in the boundary layer, orbital velocities associated with these motions can generate oscillatory sediment fluxes which have been demonstrated to be important to the net sediment transport in the surf zone.

Nearshore-standing infragravity waves may occur as either leaky mode waves which are two-dimensional standing waves having a succession of antinodes and nodes away from the point of reflection (e.g. the shoreline), or as edge waves which are three-dimensional waves trapped against the nearshore by reflection and refraction and which can propagate alongshore (progressive edge waves) or be longshore-standing (standing edge waves). Edge waves have a finite number of nodes/antinodes in the cross-shore direction (the number of cross-shore surface elevation nodes is called the mode number, [math]n[/math]), and a theoretically infinite number of nodes/antinodes in the longshore dimension.

Infragravity wave heights and orbital velocities increase towards the shoreline (see Fig. 5. below), while incident wave heights decrease landward due to wave breaking. Infragravity waves should therefore be of increasing relative importance with proximity to the shoreline and sediment resuspension and transport become increasingly affected by infragravity motions. A more comprehensive treatment of nearshore infragravity waves can be found in e.g. Aagaard and Masselink (1999)[5] and Infragravity waves.

Measurement of Waves

Waves are traditionally measured with wave rider buoys. More recently, remote sensing techniques for measuring waves have been developed, see Measuring waves and currents by X-band radar.


Related articles

Shallow-water wave theory
Statistical description of wave parameters
Infragravity waves
Tsunami
Seiche
Wave set-up
Wave transformation
Breaker index
Swash zone dynamics


References

  1. ↑ Curto, D., Franzitta, V. and Guercio, A. 2021. SeaWave Energy. A Review of the Current Technologies and Perspectives. Energies 14, 6604
  2. ↑ Cornett, A. 2008. A global wave energy resource assessment. In: Proceedings of the 18th International Offshore and Polar Engineering Conference, Vancouver, BC, Canada, 6–11 July 2008; ISOPE-2008-TPC-579, pp. 1–9
  3. ↑ Toffoli, A. and Bitner-Gregersen, E.M. 2017. Types of Ocean Surface Waves, Wave Classification. Encycl. Marit. Offshore Eng. 2017: 1–8
  4. ↑ 4.0 4.1 4.2 4.3 Written by Aagard, Troels. 2007.
  5. ↑ Aagaard, T. and Masselink, G., 1999. The Surf Zone. In: A.D.Short (ed) Handbook of Beach and Shoreface Morphodynamics, Wiley Interscience, pp.72-118.

Further reading

Mangor, K., Drønen, N. K., Kaergaard, K.H. and Kristensen, N.E. 2017. Shoreline management guidelines. DHI https://www.dhigroup.com/marine-water/ebook-shoreline-management-guidelines.


The main author of this article is Mangor, Karsten
Please note that others may also have edited the contents of this article.
Citation: Mangor, Karsten (2024): Waves. Available from http://www.coastalwiki.org/wiki/Waves [accessed on 2-05-2024]
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