The effects of a sloping bottom on the equatorial wave-induced deep residual currents

Abstract

Based on an inverted one-and-one-half inviscid reduced gravity shallow water model with bottom topography representing an abyssal layer under a stagnant upper layer on the equatorial β-plane, a set of field equations governing the wave-induced Lagrangian residual currents is developed. The equations show that the wave-induced Lagrangian residual current satisfies generalized geostrophic dynamics. The relation of meridional residual current to vertical residual current resulted from the varied bottom is similar to the Sverdrup transport relation. The transport process of potential vorticity for zeroth order approximation is determined by the advection whose velocity is equal to that of the wave-induced Lagrangian residual current.