A third-generation numerical wave model to compute random, short-crested waves in coastal regions with shallow water and ambient currents (Simulating Waves Nearshore (SWAN)) has been developed, implemented, and validated. The model is based on a Eulerian formulation of the discrete spectral balance of action density that accounts for refractive propagation over arbitrary bathymetry and current fields. It is driven by boundary conditions and local winds. As in other third-generation wave models, the processes of wind generation, whitecapping, quadruplet wave-wave interactions, and bottom dissipation are represented explicitly. In SWAN, triad wave-wave interactions and depth-induced wave breaking are added. In contrast to other third-generation wave models, the numerical propagation scheme is implicit, which implies that the computations are more economic in shallow water. The model results agree well with analytical solutions, laboratory observations, and (generalized) field observations.

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A third-generation wave model for coastal regions: 1. Model description and validation

Morphodynamic variability of surf zones and beaches: A synthesis

Development and validation of a three-dimensional morphological model

Applied Numerical Analysis. By C.F. Gerald. Pp. xii, 340. £3·60. 1970. (Addison-Wesley.)

https://oss.deltares.nl/documents/48999/59759/Roelvink_2009.pdf

Modelling storm impacts on beaches, dunes and barrier islands

Earlier models of random wave transformation are reviewed in the first section. Then the transformation of waves, including dissipation due to breaking and bottom friction, is described by an energy flux balance model. The wave height pdf of all waves (broken and unbroken) is shown by the field data to be well described by the Rayleigh distribution everywhere. The observed distributions of breaking and broken wave heights are fitted to simple analytical forms, and breaking wave dissipation is calculated by using a periodic bore formulation. The energy flux equation is integrated to yield local values of Hrms as a function of offshore wave conditions. Both analytical and numerical models are developed. In the last section the models are compared with results from random wave experiments in the laboratory and from an extensive set of field measurements.

/pdf/transformation-of-wave-height-distribution-2kl80xxt9b.pdf

Transformation of wave height distribution

Genetically, beach cusps are of at least two types: those linked with incident waves which are surging and mostly reflected (reflective systems) and those generated on beaches where wave breaking and nearshore circulation cells are important (dissipative systems). The spacings of some cusps formed under reflective wave conditions both in the laboratory and in certain selected natural situations are shown to be consistent with models hypothesizing formation by either (1) subharmonic edge waves (period twice that of the incident waves) of zero mode number or (2) synchronous (period equal to that of incident waves) edge waves of low mode. Experiments show that visible subharmonic edge wave generation occurs on nonerodable plane laboratory beaches only when the incident waves are strongly reflected at the beach, and this observation is quantified. Edge wave resonance theory and experiments suggest that synchronous potential edge wave generation can also occur on reflective beaches and is a higher-order, weaker resonance than the subharmonic type. In dissipative systems, modes of longshore periodic motion other than potential edge waves may be important in controlling the longshore scale of circulation cells and beach morphologies. On reflective plane laboratory beaches, initially large subharmonic edge waves rear-rage sand tracers into shapes which resemble natural beach cusps, but the edge wave amplitudes decrease as the cusps grow. Cusp growth is thus limited by negative feedback from the cusps to the edge wave excitation process. Small edge waves can form longshore periodic morphologies by providing destabilizing perturbations on a berm properly located in the swash zone. In this case the retreating incident wave surge is channelized into breeches in the berm caused by the edge waves, and there is an initially positive feedback from the topography to longshore periodic perturbations.

Edge waves and beach cusps

Waves, currents, and the location of the seafloor were measured on a barred beach for about 2 months at nine locations along a cross-shore transect extending 255 m from 1 to 4 m water depth The seafloor location was measured nearly continuously, even in the surf zone during storms, with sonar altimeters mounted on fixed frames The crest of a sand bar initially located about 60 m from the shoreline moved 130 m offshore (primarily when the offshore significant wave height exceeded about 2 m), with 15 m of erosion near the initial location and 1 m of accretion at the final location An energetics-type sediment transport model driven by locally measured near-bottom currents predicts the observed offshore bar migration, but not the slow onshore migration observed during low-energy wave conditions The predicted offshore bar migration is driven primarily by cross-shore gradients in predicted suspended sediment transport associated with quasi-steady, near-bottom, offshore flows These strong (>50 cm/s) currents, intensified near the bar crest by wave breaking, are predicted to cause erosion on the shoreward slope of the bar and deposition on the seaward side The feedback amoung morphology, waves, circulation, and sediment transport thus forces offshore bar migration during storms

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/97JC02765

Observations of sand bar evolution on a natural beach

Run-up (swash) oscillations were measured on a gently sloping beach face for a variety of incident wave conditions. Run-up energy spectra at wind wave frequencies show an ƒ−3 dependence and energy levels that are independent of incident wave height. This suggests saturation. In contrast, run-up energy at surf beat periods increase approximately linearly with increasing incident wave energy. Thus, in the inner surf zone, where wave breaking limits the energy at wind wave frequencies, the principal manifestation of large incident wind waves is energetic surf beat.

Swash oscillations on a natural beach

Aspects of the nonlinear dynamics of waves shoaling between 9 and 1 m water depths are elucidated via the bispectrum. The biphase values associated with significant bicoherence levels in 9 m depth are consistent with Stokes-like nonlinearities, but as the water depth decreases the waves evolve through a slightly skewed shape somewhat asymmetrical to a vertical axis toward a highly asymmetrical unskewed sawtooth shape. The real and imaginary parts of the bispectrum are the contributions to skewness and asymmetry from individual frequency pairs.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112085003007

Robert T. Guza

Papers

Transformation of wave height distribution

Edge waves and beach cusps

Observations of sand bar evolution on a natural beach

Swash oscillations on a natural beach

Observations of bispectra of shoaling surface gravity waves