Simulation of nearshore directional waves and depth-averaged currents.

Abstract

Storm generated winds and waves are responsible for significant erosion of coastal property. Waves and winds drive currents near the shore that transport sediment along and transverse to the coast. Most existing models for nearshore currents do not consider the effects of the wind on the water column and simplify the wave field by using monochromatic wave theory. The waves during a storm cannot be accurately characterized by a single representative wave, as there is finite band width in the energy spectrum for both the frequency and the directional domain. It is important to include the variation in the direction of wave approach when computing nearshore flows, particularly when the bathymetry is irregular. A numerical model is developed to predict the transformation of a wave field with directional variation of wave action, and the mean flows that result from the dissipation of the waves as they propagate shoreward. The wave action conservation equation is simplified using the first two moments of the action frequency spectrum. New expressions for the interaction of the wave directional components are derived using ensemble-averaging of the radiation stress, bottom stress and bottom dissipation terms. The simplified wave action conservation equations are solved using an alternating scheme with the momentum and continuity equations. Finite differences and an explicit space-stepping algorithm are employed. Although the magnitude of the simulated longshore currents is less than field measurements. The simulated longshore velocity agrees well with the Longuet-Higgins analytical model. The wave height transformation is well represented by the numerical model. The large variations in the current velocities across a longshore bar illustrate the bathymetric influence on the mean flows. The numerical model simulates nearshore currents and wave heights over irregular bathymetry. The simulations did not appear to accurately quantify momentum transfers from the wind to the mean flows. The comparisons improve when the wind drag coefficient is increased.