INTERNAL WAVE VORTICAL MODE INTERACTIONS IN STRONGLY STRATIFIED FLOWS

In this paper, weakly nonlinear interactions in a strongly-stratified, inviscid flow are re-examined, taking into account the presence of both internal waves and vortical modes. We use a multiple scale formulation, based on the two characteristic times of the problem. Ertel's potential vorticity motivates a splitting of the velocity into propagating (wave) and non-propagating (vortical) contributions. We focus on the three fundamental interactions: the wave/wave, wave/vortex and vortex/vortex interactions. The oft-studied wave/wave interaction illustrates the difference between potential and vertical vorticities. We then identify two additional resonances for the wave/vortex and vortex/vortex interactions respectively. The wave/vortex resonance provides a mechanism for redistributing energy in spectral space while the vortex/vortex interaction may give rise to an internal wave field.