Interaction of internal waves impinging upon stratified turbulence

In the ocean, internal wave beams are generated by the barotropic tide passing over steep topography. Observations suggest that these wave beams are dissipated as they propagate into the upper ocean. This differs from idealised numerical simulations of wave propagation, in which the wave beams often reflect off the surface. Inspired by this discrepancy, we hypothesise that wave beams in the ocean can be absorbed by stratified turbulence, inhibiting their reflection. In this idealised study we perform three-dimensional direct numerical simulations, where stratified turbulence is generated in the top half of the domain and forcing is applied near the bottom, creating upward-propagating waves with fixed frequency that travel toward the turbulent layer. We apply dynamic mode decomposition to extract the structure of disturbances at the wave-forcing frequency and then use Hilbert transforms to separate upward from downward travelling disturbances. Thus we diagnose wave reflection, should it occur. We compare results for cases in which only turbulence is present with cases in which waves are forced with different frequencies and amplitudes. Although wave reflection is observed for strongly non-hydrostatic waves, sufficiently low-frequency waves are absorbed by the turbulent layer.