PRIMITIVE EQUATION INSTABILITY OF WIDE OCEANIC RINGS .1. LINEAR-THEORY

The linear stability of two-layer primitive equation ocean rings is co nsidered in the case when the rings are wide compared with a deformati on radius, as is usually observed. Asymptotic theory is developed to s how the existence of solutions for arbitrarily wide rings, and these s olutions can be followed as the rings are made successively narrower. An exponential cubic radial dependence is used for the mean flow, rath er than the more usual Gaussian structure. There are two reasons: a Ga ussian shape was fully discussed in a previous paper, and a Gaussian h as exceptional properties, unlike other power laws. The specific cases of warm and cold Gulf Stream rings are considered in detail. The theo ry provides an accurate prediction of phase velocity and growth rate f or cold rings and a reasonable prediction for warm rings. Solutions in the asymptotic regime have a larger growth rate than other (nonasympt otic) solutions for cold rings, but not for warm rings. Attention is g iven to the role of the mean barotropic circulation, which had been fo und in earlier work to have a strong effect on ring stability. There i s still evidence for stabilization when the mean flow in the lower lay er vanishes, but other features are also involved. In particular, the linear stability of a ring appears to be as sensitive to subtle shape details as it is to the sense of the deep flow. The authors generally find warm co-rotating rings with a cubic exponential form to be unstab le, although somewhat less so than counterrotating rings.