Dispersion Effects on Longshore Currents in Surf Zones

Abstract

A time-dependent model for obliquely incident shallow-water waves with small incident angles is developed to elucidate the dispersion effects due to the vertical variations of instantaneous horizontal fluid velocities on the cross-shore variations of the wave height, setup, and longshore current in surf zones. The three equations for the cross-shore continuity, momentum, and momentum flux correction are solved numerically to predict the water depth and the cross-shore depth-averaged and near-bottom velocities. The two equations for the alongshore momentum and momentum flux correction are derived and solved to predict the alongshore depth-averaged and near-bottom velocities. The developed model is compared with laboratory and field data for planar beaches. The dispersion effects on the wave height and setup are shown to be minor. The dispersion effects on the longshore current are significant for regular waves but secondary for irregular waves. The model is also shown to predict the vertical shape of the longshore current in the surf zone but not outside the surf zone.