Decay of a mesoscale oceanic eddy: analysis of linear stability dynamics and critical levels

This study addresses the linear stability of an oceanic mesoscale eddy. A linear stability analysis of the quasi-geostrophic potential vorticity equation governing an idealized Gaussian vortex in a continuous stratification is performed, and the properties of the instability are analyzed. We show how growth of the instability is via mutual amplification of waves at different levels in the eddy, analogous to the Eady baroclinic instability. The fastest growing mode gives rise to enhanced vertical and horizontal density gradients that coincide with the critical level in the vicinity of the perturbed eddy; at this level, the mean angular speed is equal to the angular phase speed of the perturbation. We show how these enhanced density gradients relate to maximal radial water parcel displacement at the critical level. Results shed light on the physics of mesoscale eddy decay and further demonstrate the role of enhanced mixing at critical levels in the ocean.