Partial reflexion of water waves by non-uniform adverse currents

Abstract

The propagation of linearized waves on a non-uniform slowly varying potential current is studied by converting the equations of flow into a Schrödinger ordinary differential equation in the complex plane. This equation, which is solved by the WKB method, indicates the existence of current barriers which allow partial energy transmission while reflecting the complementary part. The classical result of total transmission (Longuet-Higgins & Stewart 1961) as well as that of complete reflexion (Peregrine 1976) are recovered as limiting cases by the present, more general approach.