Mean flow generation due to oblique reflection of internal waves at a slope*

A theoretical study is made of the mean flow induced by the reflection of a weakly nonlinear internal gravity wave beam at a uniform rigid slope, in the general case where the beam meets the slope at an arbitrary direction, not necessarily parallel to the isobaths, and the flow cannot be taken as 2D.  In the vertical direction, the Eulerian mean flow due to such an oblique reflection is equal and opposite to the Stokes drift, so the Lagrangian mean flow vanishes, as in a 2D reflection.  The horizontal mean flow, however, is controlled by the mean potential vorticity (PV), which in contrast to 2D does not vanish, and the horizontal Lagrangian mean flow is generally non-zero.  Furthermore, for oblique reflection, viscous dissipation can lead to resonant generation of horizontal mean flow owing to irreversible production of mean PV, a phenomenon known as streaming.