Edge waves: a long-wave theory for oceans of finite depth

Abstract

Edge waves travelling along a straight coastline are examined in the case when the water depth approaches a constant value at large distances from the coast. Only the fundamental mode is examined in the limit as the ratio of the water depth at infinity to the edge-wave wavelength tends to zero. Two comparison theorems are used to obtain upper and lower bounds for the dispersion relation. A long-wave approximation procedure is used to obtain the leading terms in the dispersion relation for a wide class of bottom topographies. The results obtained are compared with an exact result for the case when the bottom topography is a rectangular step.