Presenter: James Hilditch (Stanford University)

Description:
Observations made during the SUNRISE (Submesoscales Under Near Resonant Inertial Shear Experiment) cruise show along isopycnal shear bands in a front oscillating under inertial shear. Here we present a mechanism by which along isopycnal sub-inertial waves can be excited. In a steady balanced front, the lowest frequency inertia-gravity waves are given by along isopycnal perturbations, assuming the hydrostatic limit, since they do not feel a buoyancy force. However, the Coriolis force is also reduced and these waves will be sub-inertial. The extent of which is determined by the balanced Richardson number of the front defined as the ratio of the square of the buoyancy frequency to the square of the thermal wind shear. For balanced Richardson numbers less than 4/3 waves at half the inertial frequency are permitted and inertial oscillations are potentially unstable to parametric subharmonic instability (PSI). We construct a simple model of a front under inertial shear that allows for arbitrary perturbations, non-hydrostatic effects, and strong inertial shear. The model is unstable to PSI across a large range of parameter space and also symmetric instability (SI) for balanced Richardson numbers less than 1. Both instabilities are able to excite along isopycnal modes and are possible explanations for the shear in the observations. The unstable PSI modes can have fast, O(f), growth rates and grow through shear production. An analysis of the perturbation kinetic energy budget reveals that the ageostrophic shear production associated with the inertial shear is the dominant growth term and that the geostrophic shear production is negative for the PSI modes which is in direct contrast to the SI modes. PSI is therefore a very efficient damper of inertial oscillations and quickly drives the front towards a balanced state.