Role of background mean flow in the PSI of internal wave beams*

Parametric subharmonic instability (PSI) is believed to play a major role in the long-term fate of internal waves in stratified fluids such as the oceans and atmosphere. As PSI involves a transfer of energy from large to small scales, it is hypothesized to be a major contributor to wave dissipation and mixing. While the idealized PSI of three interacting plane waves is well understood, its applicability to realistic oceanic scenarios remains unclear and discrepancies between predictions and observations of dissipation rates remain unresolved. In particular, large-scale currents are ubiquitous in the natural environment and their effects on the dynamics of PSI are not yet well understood. To this end, we consider an internal wave beam of finite width propagating in a background mean flow and theoretically investigate its stability to fine-scale subharmonic perturbations. In a weakly nonlinear setting, we derive evolution equations for the perturbations and we find that the presence of a weak background mean flow can either weaken or enhance PSI, suggesting that the oceanic scenario may be more complex than previously thought.