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

Development and validation of a three-dimensional morphological model

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

Modelling storm impacts on beaches, dunes and barrier islands

1. Introduction 2. Observation techniques 3. Description of ocean waves 4. Statistics 5. Linear wave theory (oceanic waters) 6. Waves in oceanic waters 7. Linear wave theory (coastal waters) 8. Waves in coastal waters 9. The SWAN wave model Appendices References Index.

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Waves in Oceanic and Coastal Waters

[1] The morphodynamic response of the nearshore zone of an embayed beach induced by wave groups is examined with a numerical model. The model utilizes the nonlinear shallow water equations to phase resolve the mean and infragravity motions in combination with an advection-diffusion equation for the sediment transport. The sediment transport associated with the short-wave asymmetry is accounted for by means of a time-integrated contribution of the wave nonlinearity using stream function theory. The two-dimensional (2-D) computations consider wave group energy made up of directionally spread, short waves with a zero mean approach angle with respect to the shore normal, incident on an initially alongshore uniform barred beach. Prior to the 2-D computations, the model is calibrated with prototype flume measurements of waves, currents, and bed level changes during erosive and accretive conditions. The most prominent feature of the 2-D model computations is the development of an alongshore quasi-periodic bathymetry of shoals cut by rip channels. Without directional spreading, the smallest alongshore separation of the rip channels is obtained, and the beach response is self-organizing in nature. Introducing a small amount of directional spreading (less than 2°) results in a strong increase in the alongshore length scales as the beach response changes from self-organizing to being quasi-forced. A further increase in directional spreading leads again to smaller length scales. The hypothesized correlation between the observed rip spacing and wave group forced edge waves over the initially alongshore uniform bathymetry is not found. However, there is a correlation between the alongshore length scales of the wave group-induced quasi-steady flow circulations and the eventual alongshore spacing of the rip channels. This suggests that the scouring associated with the quasi-steady flow induced by the initial wave groups triggers the development of rip channels via a positive feedback mechanism in which the small scour holes start attracting more and more discharge.

Morphodynamic modeling of an embayed beach under wave group forcing

A prediction model for stationary, short-crested waves in shallow water with ambient currents

The numerical model SWAN (Simulating WAves Nearshore) for the computation of wave conditions in shallow water with ambient currents is briefly described. The model is based on a fully spectral representation of the action balance equation with all physical processes modelled explicitly. No a priori limitations are imposed on the spectral evolution. This makes the model a third-generation model. In Holthuijsen et al. (1993) and Ris et al. (1994) test cases for propagation, generation and dissipation have been shown without currents. Current effects have now been added and academic cases are shown here. The model is also applied in a fairly academic case of a shallow lake (Lake George, Australia) and in a complex, realistic case of an inter-tidal area with currents (Friesche Zeegat, the Netherlands). The results are compared with observations. A new development to formulate the model on a curvi-linear grid to accommodate linkage to hydro-dynamic circulation models is presented and a first test is shown.

/pdf/the-swan-wave-model-for-shallow-water-35ihy3384f.pdf

The "swan" wave model for shallow water

A note on the accuracy of the mild-slope equation

A mathematical model for the combined refraction-diffraction of linear periodic gravity waves on water is developed, in which the influence of inhomogeneities of depth and current is taken into account. The model is used to compute partial reflection of waves a gully or an undersea slope, with influence of a current. The model is also applied to prismatic wave channels with reflecting side-walls. For a gully bounded by shallows the model predicts the decay of wave height due to radiation of energy in lateral direction. For practical application in regions with arbitrary bottom and current topography a parabolic approximation of the model is derived. This is used as a basis for numerical calculation of waves in a sea region near the coast.

/pdf/gravity-waves-on-water-with-non-uniform-depth-and-current-17psa9kdfh.pdf

Gravity waves on water with non-uniform depth and current

The present paper describes the second phase in the development of a fully spectral wave model for the near shore zone (SWAN). Third-generation formulations of wave generation by wind, dissipation due to whitecapping and quadruplet wave-wave interactions are added to the processes of (refractive) propagation, bottom friction and depth-induced wave breaking that were implemented in the first phase (Holthuijsen et al., 1993). The performance and the behaviour of the SWAN model are shown in two observed cases in which waves are regenerated by the wind after a considerable decrease due to shallow water effects. In the case of the Haringvliet (a closed branch of the Rhine estuary, the Netherlands) reasonable results in terms of significant wave heights were obtained. In the case of Saginaw Bay (Lake Huron, USA), the SWAN model underestimates the significant wave height deep inside the bay (as did two other models). Due to the absence of triad wave-wave interactions in the model the mean period is not properly shifted to the higher frequencies in shallow water. Adding these triads is planned for the next phase of developing the SWAN model.

https://icce-ojs-tamu.tdl.org/icce/index.php/icce/article/download/4946/4626

N. Booij

Papers

A prediction model for stationary, short-crested waves in shallow water with ambient currents

The "swan" wave model for shallow water

A note on the accuracy of the mild-slope equation

Gravity waves on water with non-uniform depth and current

A spectral model for waves in the near shore zone