Stability of multi-layer ocean vortices: a parameter study including realistic Gulf Stream and Agulhas Rings

Ocean rings, when isolated from major ocean currents, can have life spans on the order of years. This study focuses on the stability of such isolated ocean rings. Assuming axisymmetric basic state profiles, the linear stability of a wide variety of rings is analyzed, by examining the properties of the modes to which they become unstable and the associated energy conversions.
Earlier studies have indicated that co-rotating rings, with a large barotropic component, are far less unstable than counter-rotating ones. This sharp contrast between co- and counter-rotating rings appears to be a consequence of the choice for an azimuthal velocity profile that decays only gradually on the ring\'s outer flank. For more realistic velocity profiles, co- and counter-rotating rings have similar growth rates. Nearly compensated rings, i.e. those with a weak flow in the deepest layer, are found to be the least unstable ones.
In this paper, we first revisit the problem for warm-core rings with a Gaussian profile in a two-layer set-up. A systematic survey of the sensitivity of the results for this standard case with respect to various ring parameters, like the stratification, ring width and in particular the azimuthal velocity profile, is presented. Besides exponential profiles, as used in earlier studies, we also examine the stability of rings with a core in solid-body rotation. Subsequently, we proceed towards more realistic cases by discussing the stability of ocean rings designed as fits to an observed cold-core Gulf Stream ring and a warm-core Agulhas ring. Minimal growth rates for the latter rings are quite large: the calculated e-folding time scales are about one week.