Primitive-equation instability of wide oceanic rings. Part II: Numerical studies of ring stability

The study of barotropic structure and its effects on oceanic ring stability has yielded seemingly conflicting results. Some studies suggest that the s tability of a given ring profile is as sensitive to the sense of the barotr opic mode as it is to the vertical shear, while others suggest the vertical shear is the sole dominant effect. Here numerical evidence that supports b oth views is presented. Warm rings with a favorable barotropic structure ca n retain their monopole nature while cold rings do not. These results are o f interest given the observed long lifetimes of oceanic rings. As evidence a series of initial value integrations is presented. The initia l ring profile consists of an exponential profile decaying as the cube of t he radial distance, rather than as the squared decay law of the commonly us ed Gaussian. The reasons for this choice are that previous studies have exa mined the Gaussian initial condition extensively and recent analysis sugges ts the Gaussian profile has special stability properties. The authors find that the barotropic mode affects the coherence of warm rin gs, yielding essentially stable, monopolar structures for the case that the initial deep flow is in the same sense as the surface how (i.e., in the "c o-rotating" case), even if the initial underlying ring is linearly unstable . Thus, warm rings remain dominantly monopolar, although an underlying, wea k tripole is often seen in the final state. Cold rings in the oceanic param eter regime, on the other hand, experience no such stabilizing effects from deep structure. Quasigeostrophic dynamics fails to capture the stabilizati on tendencies of warm rings with corotating deep flow, suggesting the effec t is related to the finite-amplitude thickness changes of a warm ring. The transition from an unstable, warm monopolar initial state to an effectively stable, warm initial monopolar state is a sensitive function of the barotr opic mode. Finally, beta-plane experiments demonstrate the robustness of th e primitive equation result. Thus, it is suggested that the barotropic component of a warm ring can enha nce ring stability as a monopole by providing for the existence of a nearby tripolar state to which the ring evolves and thereafter remains. The obser ved stability of cold rings, however, remains a mystery.