A direct comparison of a depth-dependent Radiation stress formulation and a Vortex force formulation within a three-dimensional coastal ocean model.

Abstract: In this study a model system consisting of the three-dimensional General Estuarine Transport Model (GETM) and the third generation wind wave model SWAN was developed. Both models were coupled in two-way mode. The effects of waves were included into the ocean model by implementing the depth-dependent Radiation stress formulation (RS) of Mellor (2011a) and the Vortex force formulation (VF) presented by Bennis et al. (2011). Thus, the developed model system offers a direct comparison of these two formulations. The enhancement of the vertical eddy viscosity due to the energy transfer by white capping and breaking waves was taken into account by means of injecting turbulent kinetic energy at the surface. Wave-current interaction inside the bottom boundary layer was considered as well. The implementation of both wave-averaged formulations was validated against three flume experiments. One of these experiments with long period surface waves (swell), had not been evaluated before. The validation showed the capability of the model system to reproduce the three-dimensional interaction of waves and currents. For the flume test cases the wave-induced water level changes (wave set-up and set-down) and the corresponding depth-integrated wave-averaged velocities were similar for RS and VF. Both formulations produced comparable velocity profiles for short period waves. However, for large period waves, VF overestimated the wave set-down near the main breaking points and RS showed artificial offshore-directed transport at the surface where wave shoaling was taking place. Finally the validated model system was applied to a realistic barred beach scenario. For RS and VF the resulting velocity profiles were similar after being significantly improved by a roller evolution method. Both wave-averaged formulations generally provided similar results, but some shortcomings were revealed. Although VF partly showed significant deviations from the measurements, its results were still physically reasonable. In contrast, RS showed unrealistic offshore-directed transport in the wave-shoaling regions and close to steep bathymetry. [Copyright &y& Elsevier]