Vortex scattering by step topography

Abstract

The scattering at a rectilinear step change in depth of a shallow-water vortex pair consisting of two patches of equal but opposite-signed vorticity is studied. Using the constants of motion, an explicit relationship is derived relating the angle of incidence to the refracted angle after crossing. A pair colliding with a step from deep water crosses the escarpment and subsequently propagates in shallow water refracted towards the normal to the escarpment. A pair colliding with a step from shallow water either crosses and propagates in deep water refracted away from the normal or, does not cross the step and is instead totally internally reflected by the escarpment. For large depth changes, numerical computations show that the coherence of the vortex pair is lost on encountering the escarpment.