The effect of ageostrophy on the stability of thin oceanic vortices

This paper examines the stability of vortices in a two-layer ocean on the f-plane. The mean depth h¯1 of the upper layer is assumed to be much smaller than the depth h¯2 of the lower layer. Using the primitive equations, we derive an asymptotic criterion for baroclinic instability of compensated (i.e. confined to the upper layer) vortices. Surprisingly, it coincides exactly with a similar criterion derived from the quasigeostrophic equations [Benilov, E.S., 2003. Instability of quasigeostrophic vortices in a two-layer ocean with thin upper layer. J. Fluid Mech. 475, 303-331]. Thus, to leading order in h¯1/h¯2, ageostrophy does not affect the stability properties of thin compensated vortices. As a result, whether a vortex is stable or not, depends on its shape, not amplitude (although the growth rate of an unstable vortex does depend on its amplitude).