Decay of Stable Warm-Core Eddies in a Layered Frontal Model

Abstract

Aspects of the decay of stable frontal warm-core eddies in the deep ocean are investigated using a new numerical layered ?frontal? model that solves the nonlinear, reduced-gravity, shallow-water equations for a horizontally inhomogeneous, viscous fluid on an f plane. After a discussion on aspects of the numerical techniques implemented to allow for the eddy expansions and contractions at the sea surface, for the first time the capability of a numerical model of reproducing the evolution of analytical nonstationary frontal vortices is explored. This step is necessary, as far as different phenomena related to the dynamics of these oceanic features are to be studied numerically. In fact the comparison between numerical and analytical inviscid solutions allows for a quantification of the numerical dissipation affecting the simulated solutions. This dissipation is found to be very small in this numerical model: The simulated lifetimes are larger than those of most of the frontal eddies observed in the World Ocean. On this basis, the eddy decay due to interfacial (linear and quadratic) friction, harmonic horizontal momentum diffusion, as well as linear ambient-water entrainment is investigated. It is found that interfacial friction represents a much more efficient mechanism than horizontal diffusion and water entrainment in inducing the eddy decay as well as in damping the eddy pulsations. It is thus suggested that internal wave radiation due to vortex pulsation can represent a relevant mechanism for the dissipation of the vortex energy in a stratified ambient ocean only episodically. Finally, a critical discussion about the appropriateness of the different approximations assumed in the investigation is presented. In particular, the appropriateness of the reduced-gravity assumption is discussed. Results are consistent with those obtained analytically in the frame of the frontal-geostrophic theory: Although the effect of an active ambient layer on the vortex dynamics is found to be virtually absent only for unrealistically large water depths, it appears that the reduced-gravity model describes warm-core eddies acceptably for values of the ratio between maximum vortex thickness and total water depth typical for Gulf Stream rings.