The transmission of deep-water waves across a vortex sheet

Abstract

The effect on an obliquely incident surface wave of a vortex sheet separating two uniform currents is considered. It is shown that the amplitude of the transmitted wave as a function of the angle of incidence and current strength is very close to that obtained by Longuet-Higgins & Stewart on the assumption of small smooth changes in current velocity. The difference is accounted for by a small amount of reflexion of the wave by the vortex sheet. It is suggested that, in the intermediate range where the change in current velocity over a wavelength is comparable with the wave velocity, the wave amplitude of the transmitted wave lies between the curves of Longuet-Higgins & Stewart and those found here.