Near-inertial parametric subharmonic instability of internal wave beams in a background mean flow

The effect of a small background constant horizontal mean flow on the parametric subharmonic instability (PSI) of locally confined internal wave beams is discussed for the case where the beam frequency is close to twice the inertial frequency due to background rotation. Under this condition, PSI is particularly potent because of the vanishing of the group velocity at the inertial frequency, which prolongs contact of near-inertial subharmonic perturbations with the primary wave. The mean flow generally stabilizes the very short-scale limit of such perturbations. By contrast, the stability of longer-scale perturbations hinges on the strength and the direction of the mean flow; particularly, a negative mean flow (antiparallel to the horizontal projection of the beam group velocity) can extend the sub-inertial range of PSI. However, a large enough mean flow of either sign ultimately weakens PSI.