A Three-Dimensional Numerical Model of Surface Waves in the Surf Zone and Longshore Current Generation over a Plane Beach

Abstract

A three-dimensional numerical model is developed for the propagation of shallow-water short-period surface waves in the surf zone and longshore current generation over a plane beach topography. This model, which is based on Reynolds-averaged non-linear shallow-water (NSW) equations and, hence, includesimplicitlythe classical radiation stress concept, resolves time- and space-dependence of the sea surface elevation and the velocity fields during one wave cycle (short-wave-resolving). The generation of turbulence by wave breaking and vertical fluid shear above the beach is parameterized by the application of a generalized turbulence energy closure scheme. The instantaneous position of the moving shoreline is determined from the model equations during the simulated propagation process. In the case of a single incoming wave train, the wave amplitude, wave period and angle of incidence are prescribed at an offshore open boundary by application of a forced radiation condition. For uniform alongshore topographic conditions, when cyclic boundary conditions are appropriate at alongshore open boundaries whose positions are determined by the alongshore component of wavelength in an incoming single wave train, the model is used to determine the (mean) longshore current during one wave cycle. It is shown that the maximum longshore depth-averaged current occurs at an approximate offshore position where the generation of turbulence energy through wave breaking is a maximum. It is further shown that the cross-shore gradient of the longshore momentum flux is of predominant importance in generating longshore currents. Experiments are described that determine the dependence of the computed longshore current on the bottom roughness and the length scale prescription in that part of the turbulence closure scheme pertaining to the parameterization of the wave breaking process. The implications of the model results are discussed in the context of the longshore bedload transport of sedimentary material. Finally, a comparison is made between the model predictions and observational data on longshore currents and wave heights.