Oblique reflections of internal gravity wave beams

Abstract

We study nonlinear effects in reflections of internal gravity wave beams in a continuously stratified liquid which are incident upon a uniform slope at an oblique angle. Wave motion in a stratified fluid medium is unique in the sense that the anisotropy of stratification directs energy transport in a manner specified by the frequency of the driving mechanism. Since there is no spatial variation along the direction of the flow field, plane waves are exact nonlinear solutions of the governing equations. In general, energy is carried in the form of a wave beam, which is a superposition of plane waves having parallel wavevectors. However, beams incident upon a surface interact with the re reflected beam in a locally confined region. Nonlinear interactions in the vicinity of the reflection site where the incident and reflected beams overlap act as a source for the generation of higher order harmonics. Employing small-amplitude expansions, we determine the directions of propagation and the strength of primary and second-harmonic reflected beams. The energy associated with the secondary beam during steady-state conditions is also computed. We find that in-plane reflections produce the strongest nonlinear reflections and that larger spatial variations of the incident beam profile produce stronger secondary beams.