Inertial instability of oceanic submesoscale vortices: Marginal stability criterion, laboratory experiments and observations

Inertial instability is a possible mechanism for vertical mixing in the submesoscale ocean. The stability of axisymmetric oceanic-like vortices to inertial perturbations is investigated by linear stability analysis, taking into account the thickness and the stratification of the thermocline, as well as the vertical eddy viscosity. Numerical analysis reveals that the instability is insensitive to the vorticity profile, when using the vortex Rossby number (instead of the local normalized vorticity) as the parameter for vortex intensity. This allows extending our analytical solutions for the Rankine vortex to a wide variety of oceanic cases, including results such as the analytic dispersion relation, and the marginal stability criterion. This suits oceanic conditions better than the widely used inviscid generalized Rayleigh criterion. We corroborate our findings with large-scale laboratory experiments and find a signature of the instability on the mean-flow, which could be used in future oceanographic measurements. Finally, we discuss previously published oceanographic data in light of these results.