Current effects on resonant reflection of surface water waves by sand bars

Abstract

The effect of currents flowing across a bar field on resonant reflection of surface waves by the bars is investigated. Using a multiple-scale expansion, evolution equations for the amplitudes of linear waves are derived and used to investigate the reflection of periodic wave trains with steady amplitude for both normal and oblique incidence. The presence of a current is found to shift resonant frequencies by possibly significant amounts and is also found to enhance reflection of waves by bar fields due to the additional effect of the perturbed current field.