Stability and mixing of shear layers forced by standing internal waves

Turbulence generated by breaking internal waves is an important source of mixing in the ocean interior, and is often interpreted in terms of the stability of the vertical shear. However, observations and numerical studies suggest that vertical internal wave strain may also play a key role in stratified flow stability. Here we model the effects of wave strain by imposing a spatiallyand temporally-periodic standing wave onto a stably-stratified shear flow. To examine the linear stability of this flow, we compute optimal perturbations for a range of target times, wave amplitudes, and stratifications. The standing wave catalyzes perturbation growth in the shear layer, leading to enhanced energy gains. We then perform direct numerical simulations to examine the nonlinear perturbation evolution. We find that in some cases the linear growth is sufficient to trigger nonlinear effects and transition to turbulence. The mixing efficiency varies in time with the background wave, suggesting that the phase of the flow may be an important parameter in describing the mixing.