Swash

Definition of Swash: Propagation of thin sheets of seawater up and down the beach, after the collapse of waves on the beach face. Swash is the decelerating uprush phase and backwash is the accelerating downrush phase. This is the common definition for Swash, other definitions can be discussed in the article

Fig. 1. Swash on a reflective beach, Avoca Beach, NSW, Australia. In the background, a wave collapses on the beach; the swash uprush reaches the top of the beach berm. Photo credit: Dr Hannah Power, University of Newcastle, NSW, Australia.

Beach face

When incident waves collapse on the beach face, a thin seawater layer rushes up the beach in the swash zone situated between the surf zone and the dry beach (Fig. 1). The swash zone is often a steeper part of the beach (especially in the case of coarse-grained sediment) bordered by a beach berm at the landward side. Swash motion is a crucial link between the hydrosedimentary processes in the surf zone and the morphology (sand volume, shape) of the backshore.

Swash motion can be quite strong. Maximum uprush velocities up to 3 m/s have been measured on steep sandy foreshores and up to 2 m/s on gently sloping foreshores, while backwash velocities can attain more than 2 m/s. Uprush suspended sediment concentrations on steep and dissipative beaches can approach or exceed 100 g/l. The net sediment transport of a single swash event can cause fluctuations in beach level (accretion or erosion) by up to several centimeters. The net bed level change over an entire tidal cycle is often not much larger (less than an order of magnitude) than the change by individual swash events.

While easily observed and experienced by anyone walking along the beach, measuring the hydrodynamic characteristics of swash motion is not easy at all because of its small scale and highly unsteady nature. Swash motion is driven by waves collapsing on the beach which supply initial momentum to the wave uprush along with an amount of suspended sediment. This complex boundary condition, given the irregular character of the incident wave field, is not the only challenge for modelling the swash dynamics. The up and down flowing fluid sheets induce pore water pressure gradients with alternating upward and downward seepage that promotes destabilization of the sediment bed and transport of suspended liquefied sediments. The capability of process-based models to simulate these fine-scale processes is very limited. The contribution of swash motion to maximum water uprush (see wave run-up) and to beach accretion and erosion processes is therefore mainly based on empirical relationships. General trends can be fairly well described by these relationships, but field data are widely scattered around these trends. See the article Swash zone dynamics for a more detailed discussion.

On dissipative coasts swash processes are dominated by infragravity waves.

Swash sedimentation and erosion

The sediment suspended in the surf zone and eroded from the lower beach face is deposited at the higher beach face, where the uprush velocity is small. Deposition is enhanced by infiltration, in particular for coarse sediment beaches with average grain size [math]d_{50}[/math] larger than 1 mm. Infiltration has two opposite effects on the bed shear stress: a decrease due to reduction of the flow volume and an increase due to thinning of the boundary layer. After reaching the highest point on the beach face, the water retreats along the beach slope in a very thin layer. This so-called downrush or backwash takes sediment from the upper beach face to the lower beach face. The backwash period is generally longer than the uprush period and the velocity is lower. During the late stage of the backwash a thick sheet flow layer is formed which decreases immediately after the arrival of the next incident bore.

Exfiltration near the shoreline has two opposite effects: thickening of the boundary layer and related decrease of the bed shear stress versus bed destabilisation trough liquefaction of the bed soil layer. Laboratory experiments show that bed shear stresses are similar for impermeable and permeable beaches of fine/medium sand, whereas higher bed shear stresses are observed for permeable gravel beaches . Field observations suggest that the net effect of infiltration/exfiltration depends on grain size: for medium sediment, it decreases the uprush sediment flux ([math]\approx -10 \%[/math]) and increases the downrush sediment flux ([math]\approx 5 \%[/math]); for coarse sediment the effect is opposite.

Fig. 2. Schematic representation of swash uprush on the beach face. The vertical scale is strongly exaggerated. The swash excursion [math]X_s[/math] extends landward from the location where the incident wave bore collapses.

Entrainment of the bed top layer (1-2 cm) contributes significantly to the uprush and downrush sediment fluxes . Most of the sediment deposited by the uprush is remobilized by the backwash. Large sediment concentrations and sediment fluxes have been measured at the beginning of the uprush and last stage of the backwash. The highest deposits may remain unaffected because of scour lag; the backwash has already retreated below these deposits when it reaches velocities that are high enough for remobilization. The highest uprush deposits form a beach berm, see Fig. 2. Under extreme storms the beach berm evolves into a ridge on the upper beach .

Field experiments by Masselink et al. (2009) showed that net accretion or erosion can be very different for successive individual swash events. They found that one single swash event could contribute significantly to the net accretion or erosion occurring over a complete tidal cycle. This illustrates the difficulty of simulating swash-induced accretion or sedimentation with process-based numerical models.

Holland and Puleo (2001) presented field evidence for the following scenario of negative morphodynamic feedback to the swash process. If the swash period [math]T_s[/math] is shorter than the average period [math]T[/math] of the incoming waves, the backwash transports beach sediment to the surf zone. In such a situation the net result of swash is beach erosion. The beach face is lowered and the slope decreases. However, according to the ballistic model Eq. (A4), a decrease of the beach slope induces an increase of the uprush period. If the swash period [math]T_s = T_u +T_b[/math] is longer than the average wave period [math]T[/math], the backwash collides with the next uprush. This reduces offshore transport by the backwash; the net result of swash is now beach accretion. When the beach face accretes, the slope increases and the swash period decreases. An equilibrium slope of the beach face slope then may result such that the periods [math]T_s [/math] and [math]T[/math] are of similar duration.

Observations show that swash periods are not very different from the average period of incident waves at many reflective beaches. However, as mentioned before, long-term equilibrium does not only depend on swash processes, but also on surf processes (wave breaking on the beach) during storm periods .

The above feedback mechanism does not account for the dependence of beach slope on grain size. However, such a dependence may be expected, because swash on coarse-grained beaches is more strongly influenced by infiltration and exfiltration. Coarse sediment settles more easily at the end of the uprush than fine sediment; equilibrium with downslope transport by backwash therefore requires a steep beach slope. Hence, coarse-grained beaches (gravel beaches, for instance) typically have a steeper slope than fine- or medium-grained beaches.

The formation of beach cusps is intimately linked to the swash process. This is dealt with in the article Beach cusps.

Infragravity swash

On gently sloping dissipative beaches incident short waves lose most of their energy by breaking in the surf zone . Near the shoreline, only the longest waves survive, the so-called infragravity waves. Infragravity waves arise mainly from nonlinear interactions between short waves with different wavelengths and frequencies , see the article Infragravity waves. They carry only a small part of the wave energy on the lower shoreface (typically of the order of 1[math]\%[/math] or less), but their relative importance increases strongly in the surf zone. Infragravity waves dominate the swash motion on dissipative beaches. Empirical formulas for run-up of infragravity waves are given in the article Wave run-up.

While there is strong evidence that short-wave swash stimulates beach accretion, this is less clear for infragravity swash. Observations point to a net offshore directed transport by infragravity swash, especially in the seaward part of the swash zone. However, reliable models for simulating the complicated infragravity morphodynamics in the surf zone are not yet available .

Swash saturation

Laboratory and field observations show that the run-up [math]R[/math] is bound to a maximum value for high wave heights ([math]H[/math] of the order of 5 m or more). This is called 'swash saturation'. This can be due to wave breaking in the surf zone or breaking of infragravity waves on the beach. It can also be due to collision of the uprush with the preceding backwash, see the article Swash zone dynamics. Collision occurs when the swash period [math]T_s[/math] is longer than the period [math]T[/math] of the incident waves. Assuming [math]T_b \approx T_u[/math], then the backwash collision saturation criterium is [math]2 T_u \lt T[/math]. This implies for the maximum run-up (uprush length) a saturation limit [math]R_s[/math], according to the frictionless ballistic model (Eq. A2), [math]\qquad R \lt R_s \approx \large\frac{1}{8}\normalsize g \beta^2 T^2 \, . \qquad (1)[/math]

Appendix: Ballistic swash model

In the case of monochromatic non-breaking incident waves (usually infragravity waves), the frictionless cross-shore vertical run-up [math]R[/math] on a beach with constant slope [math]\beta[/math] can be determined analytically, see the article Waves on a sloping bed. Such non-broken waves are reflected at the shoreline and form with the incident waves a pattern of standing waves. In the case of oblique wave incidence, these reflected waves can for a pattern of edge waves.

Here we consider the more usual case of dissipative or partially reflective beaches, where incident waves collapse on the beach face and rush up as a bore, see Fig. 2. The velocity [math]V[/math] of a collapsing wave front can be estimated from the bore formula [math]\; V=2\sqrt{gD_0} \, ,[/math] where [math]D_0[/math] is the height of the collapsing wave (see Dam break flow). This assumes that all the energy of the collapsing wave is transferred to the uprush; the actual uprush velocity is generally somewhat lower.

Swash motion can be described with reasonable accuracy with a simple model based on ballistic theory. A short introduction to the ballistic model is given below.

The horizontal position of the bore front is described by the trajectory [math]x(t)[/math] up and down the beach (Fig. 2). The time [math]t=0[/math] corresponds to the wave collapse, that generates at [math]x=0[/math] a bore with speed [math] dx/dt = V \approx 2\sqrt{gD_0}[/math]. If friction and infiltration are neglected, the trajectory [math]x(t)[/math] follows the ballistic equation

[math]\Large\frac{d^2 x}{dt^2}\normalsize = - g \beta \, , \quad x(t) = - \large\frac{1}{2}\normalsize g \beta t^2 + V\, t \, , \qquad (A1)[/math]

where [math]\beta[/math] is the slope of the beach face ([math]\beta \lt \lt 1[/math]). At the end of the uprush, [math]dx/dt=0[/math]. The uprush duration is thus given by [math]T_u \approx V / g \beta [/math]. In the frictionless case, the uprush duration [math]T_u[/math] and backwash duration [math]T_b[/math] are equal; the swash period [math]T_s = T_u+T_b[/math] is thus about twice the uprush duration. The horizontal run-up is given by [math]X_s = \large\frac{1}{2}\normalsize g \beta T_u^2 = \Large\frac{V^2 }{2g \beta}\normalsize = \Large\frac{2 D_0}{\beta}\normalsize[/math] and the vertical run-up by [math]R = \beta X_s = \large\frac{1}{2}\normalsize g \beta^2 T_u^2 = 2 D_0 \, . \qquad (A2)[/math].

The uprush loses energy by turbulent overturning at the bore front and by bed friction behind the front . The velocities in the boundary layer of uprush and backwash have approximately a logarithmic profile with a friction coefficient of the order of [math]c_D \approx 0.02-0.025[/math] .

A more accurate expression is found for the run-up by including a quadratic friction term in the ballistic equation (A1),

[math]\Large\frac{d^2 x}{dt^2}\normalsize = - g \beta - \Large\frac{c_D}{D} \big( \frac{dx}{dt}\normalsize \big)^2 \, . \qquad (A3)[/math]

This nonlinear equation can be solved analytically (by separation of variables), if the thickness [math]D[/math] of the bore is assumed constant in space and time. The solutions for the uprush period [math]T_u[/math] and the run-up [math]R[/math] are

[math]T_u = \sqrt{ \Large\frac{D}{g \beta c_D}\normalsize} \tan^{-1} K , \quad R = - \Large\frac{\beta D}{c_D}\normalsize \ln (\cos(\tan^{-1} K) ) , \quad K = 2 \sqrt{\Large\frac{c_D D_0}{\beta D}\normalsize} \, . \qquad (A4) [/math]

With [math]c_D=[/math]0.025, a beach slope [math]\beta=[/math] 0.1, and with initial and average bore heights [math]D_0=[/math]0.5 m and [math]D=[/math]0.1 m, respectively, the friction reduces the uprush period [math]T_u[/math] from 4.5 s to 2.3 s and the run-up [math]R[/math] from 1 m to 0.36 m. For strong friction and gentle slopes (dissipative beaches), [math]K[/math] is generally much larger than 1 and we can approximate [math]\tan^{-1} K \approx \pi /2 - \epsilon[/math] with [math]\epsilon \lt \lt 1[/math]. The uprush period [math]T_u[/math] and run-up [math]R[/math] are then related by

[math]R \approx - \Large\frac{4 \ln \epsilon}{\pi^2 }\normalsize g \beta^2 T_u^2 \, . \qquad (A5) [/math]

This relationship is similar to that of the frictionless case (Eq. A2), apart from much shorter uprush times [math]T_u[/math]. The factor [math]- \ln \epsilon[/math] has values typically between 1 and 1.5. Experiments show that the duration of backwash [math]T_b[/math] is longer than the duration [math]T_u[/math] of uprush by 20-40[math]\%[/math] .

The run-up Eq. (A1) is related to the bore thickness estimates [math]D_0[/math] and [math]D(x,t)[/math], which depend on the height and period of the incident waves and on wave dissipation in the surf zone. Because no theoretical expression is available, empirical relationships for [math]R[/math] are used in practice, see Wave run-up.

Related articles

Swash zone dynamics

Wave run-up

Wave breaking

Waves on a sloping bed

Beach cusps

Breaker index

References

The main author of this article is Job Dronkers Please note that others may also have edited the contents of this article. Citation: Job Dronkers (2025): Swash. Available from http://www.coastalwiki.org/wiki/Swash [accessed on 21-01-2025] For other articles by this author see Category:Articles by Job Dronkers For an overview of contributions by this author see Special:Contributions/Dronkers J