Low-Frequency Barotropic Scattering on a Shelf Bordering an Ocean

Abstract

BY restricting attention to low frequencies this note solves the problem of continental shelf waves scattered at an abrupt change in width of an exponential shelf abutting a flat open ocean. Short reflected waves are treated by removing their rapid phase variation to leave an envelope governed by the long-wave equation with the direction of propagation reversed. In all cases a weak flow is forced in the open ocean by the width change. This flow is strongest for narrowing and terminating shelves, which are discussed in detail. Energy is conserved with the flux across any cross-shelf plane given by the difference between the energy carried by the long waves and the energy carried in the opposite direction by the envelope of short waves.