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.

/pdf/a-third-generation-wave-model-for-coastal-regions-1-model-37o6uqb942.pdf

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

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.

/pdf/waves-in-oceanic-and-coastal-waters-6ofdu4icqi.pdf

Waves in Oceanic and Coastal Waters

Calibration and verification of a spectral wind–wave model for Lake Okeechobee

The energy transfer equation for wind-generated ocean waves is solved numerically for fetch-limited conditions in waters of limited depth. The resulting growth curves for the total energy and the peak frequency are obtained for five different bottom friction dissipation formulations: an empirical Joint North Sea Wave Project (JONSWAP) expression (Hasselmann et al., 1973), three expressions based on the drag law friction model (Hasselmann and Collins, 1968; Collins, 1972; Madsen et al., 1988a) and a form based on the eddy viscosity friction model (Weber, 1991a). The effects of different bottom friction dissipation formulations on the energy balance are intercompared and evaluated. The results are also compared with the Coastal Engineering Research Center growth curves. Numerical simulation and mathematical analysis show that only the drag law formulations with a fixed drag coefficient scale in terms of the air friction velocity. The empirical JONSWAP, the drag law formulation with dynamically changing drag coefficient, and the eddy viscosity model do not scale. It is possible to tune the dissipation coefficients for one particular wind friction velocity but different water depths so that all five formulations give almost the same growth curves for the total energy and the peak frequency. This can be explained by the fact that the five tuned bottom friction dissipation models have the same effect on the energy balance when integrated over the frequency and angle space.

Effects of the bottom friction formulation on the energy balance for gravity waves in shallow water

On the importance of high frequency tail in third generation wave models

Field data obtained in the measurement of typhoon-generated waves in Gulf of Bei Bu, a semi-enclosed shallow water bay, is used in the validation of a 'third generation' spectral model which employs an accurate numerical solution algorithm. The linear bottom dissipation expression obtained in the JONSWAP study is adopted since it produces a more reasonable wave growth characteristics in an ideal test case as compared to the dissipation formulation based on quadratic friction law. Computational efficiency of the model is enhanced by employing digital filtering technique to suppress the numerical instability arisen from using large time step (up to about 30 minutes) and to maintain an acceptable accuracy. The performance of the model is good and provides a further support to the 'third generation' formulation of spectral models.

Spectral modelling of typhoon-generated waves in shallow waters

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Spectral modelling of typhoon-generated waves in shallow waters