Continental Shelf Wave Scattering by a Rigid Barrier Normal to the Coast

Abstract

In this paper we consider the scattering of continental shelf waves by a rigid barrier, within the context of the nondivergent, barotropic approximation. An incident wave mode encounters a rigid barrier, normal to the coast, and is scattered into a finite number of reflected wave modes and an infinite set of evanescent wave modes. The evanescent wave modes consist of two branches, a shelf branch and an ocean branch. This latter branch does not seem to have been previously identified in the literature, and is needed here to counter the flow field induced by the incident wave mode at the rigid barrier in the ocean region. The solution is constructed approximately using a Galerkin method at the rigid barrier. It is found that except near the barrier the flow field is dominated by the incident wave and the reflected wave of the same mode number, and has the appearance of an amplitude modulated wave.