ON THE STABILITY OF OCEANIC RINGS

Oceanic rings tend to have length scales larger than the deformation r adius and also to be long-lived. This latter characteristic, in view o f the former, is particularly curious as many quasigeostrophic and pri mitive equation simulations suggest such eddies are quite unstable. La rge eddies eventually break into smaller deformation scale vortices, w ith the attendant production of considerable variability. Here it is a rgued that the stability characteristics of oceanic eddies and rings a re sensitive to the presence of deep flows. In particular, eddies in w hich the deep flow is counter to the sense of the shallow flows are of ten more unstable than eddies with no deep flow, while eddies with cir culations in the same sense as the shallow circulation can experience an enhanced stability. For a given vertical shear, oceanic eddy stabil ity can vary dramatically. (This is in contrast to quasigeostrophic th eory, where stability properties are largely determined by vertical sh ear.) The onset of these mechanics is quite pronounced for Gaussian oc eanic eddies. Linear ''f''-plane stability calculations reveal a marke d suppression of unstable growth rates for warm corotating eddies with relatively weak deep flows. Cold eddies also experience a suppression of instability in the corotating state, although relatively weak unst able modes have been found. Comparisons of f- and beta-plane numerical primitive equation experiments support these results, as well as demo nstrate some relevant limitations. Finally, studies of dipolar eddies and non-Gaussian circular eddies are used to examine the generality of the results, We suggest such stability considerations may be partiall y responsible for the observed long lives of oceanic rings. An examina tion of the unstable normal modes from the f-plane model demonstrates an intimate coupling between the suppression of instability and the ap pearance of multiple critical layers. The normal-mode energetics are u sed to demonstrate the role of upgradient momentum fluxes at the point s of stabilization, and a heuristic argument involving critical layers is given.