The effect of ageostrophy on the stability of vortices in a two-layer ocean

We present a numerical study of stability of two-layer isolated vortices on the f-plane with respect to normal modes, i.e. disturbances with harmonic dependence on the azimuthal angle and time. Two types of vortices are considered: compensated vortices (for which the lower-layer is at rest), and vortices with uniform potential vorticity in the lower layer (for which a weak co-rotating circulation exists in the lower layer). It is demonstrated that, if the upper-layer is thin, the numerical results agree with the earlier asymptotic results namely, that the latter type of vortex is stable within a wide range of parameter and, thus, can account for the observed longevity of oceanic eddies. Compensated vortices, in turn, are typically unstable, with ageostrophic effects strengthening the instability for cyclones and weakening it for anticyclones. We also demonstrate that, under relatively loose assumptions, Ripa's [Ripa, P., 1989. On the stability of ocean vortices. In: Nihoul, J.C.J., Jamart, B.M. (Eds.), Mesoscale/Synoptic Coherent Structures in Geophysical Turbulence: Proceedings of the 20th International Liège Colloquium on Ocean Hydrodynamics, Elsevier Oceanography Series, vol. 50. Elsevier, Amsterdam, p. 167] stability criterion does not hold for oceanic vortices with realistic parameters.