On the Interactions of Internal Waves Reflecting from Slopes

Abstract

Incident internal waves and those reflected from a uniform slope interact at second order. These interactions are considered for incident waves traveling obliquely to the slope in a uniformly stratified rotating fluid. It is found that (i) resonant interactions cannot occur unless the inclination of the slope to the horizontal, α, is less than the inclination of the wave group velocity vector to the horizontal, ?; (ii) interactions generate a nonzero Eulerian upslope flow, which is exactly balanced by a Stokes drift, so leading to zero Lagrangian upslope flow; (iii) a Stokes drift parallel to the isobaths is generated by the reflecting waves, provided the incident waves are not in a plane normal to the slope. This drift is in addition to the possible Eulerian flows along the slope, which are in geostrophic balance with a correspondingly perturbed density field and are zero in a nonrotating flow. The order of magnitude of the drift is typically 0.01 m s?1. These secondary flows do not depend on dissipation and are therefore distinct from alongslope currents associated with wave breaking in an ?internal surf zone.?