Effects of surface waves on wind-driven current in a shallow water

We present here a theory that incorporates the effects of both the bottom wave boundary layer and the wave-induced mean Reynolds stresses for the study of the wind-driven current in shallow water. The wind is assumed steady and uniform over the fetch. A simple variable eddy viscosity is used to model the Reynolds stress and the Grant and Madsen model (1986) is selected to treat the bottom wave-current boundary layer. The stratification and Earth rotation is not considered. Numerical examples are presented for the idealized long, shallow channels. By comparing the velocity distributions obtained with and without the inclusion of the wave-induced Reynolds stresses in the model, it is shown that wave-induced mean Reynolds stresses have non-negligible effects on the velocity distribution of the wind-driven current, flushing of the channel and the wind set-up of the mean water surface.