On mean flow generation due to oblique reflection of internal waves at a slope

Abstract

Small-amplitude expansions are utilized to discuss the mean flow induced by the reflection of a weakly nonlinear internal gravity wave beam at a uniform rigid slope, in the case where the beam planes of constant phase meet the slope at an arbitrary direction, not necessarily parallel to the isobaths, and the flow cannot be taken as two dimensional. Along the vertical, the Eulerian mean flow, due to such an oblique reflection, is equal and opposite to the Stokes drift so the Lagrangian mean flow vanishes, similar to a two-dimensional reflection. The horizontal Eulerian mean flow, however, is controlled by the mean potential vorticity (PV) and the corresponding Lagrangian mean flow is generally nonzero, in contrast to two-dimensional flow where PV identically vanishes. For an oblique reflection, furthermore, viscous dissipation can trigger generation of horizontal mean flow via irreversible production of mean PV, a phenomenon akin to streaming.