Influence of topography on the dynamics of baroclinic oceanic eddies

Abstract

In this work we study motion of a baroclinic upper-ocean eddy over a large-scale topography which simulates a continental slope. We use a quasigeostrophic f-plane approximation with continuous stratification. To study this problem we develop a new numerical technique which we call "semi-lagrangian contour dynamics". This technique resembles the traditional 2-D contour dynamics method but differs significantly from it in the numerical algorithm. In addition to "Lagrangian" moving contours it includes an underlying "Eulerian" regular grid to which vorticity or density fields are interpolated. To study topographic interactions in a continuously stratified model we use density contours at the bottom in a similar manner as vorticity contours are used in the standard contour dynamics. For the case of a localized upper-ocean vortex moving over a sloping bottom the problem becomes computationally 2-dimensional (we need to follow only bottom density contours and the position of the vortex itself) although the physical domain is still 3-dimensional. Results of the numerical model lndicate importance of baroclinic effects in the vortex-topography interaction. After the initial surge of topographic Rossby waves a vortex moves almost steadily due to the interaction with a bottom density anomaly which is created and supported by a vortex itself. This anomaly is equivalent to a region of opposite-signed vorticity with a total circulation exactly compensating that of a vortex. This results in a vertically aligned dipolar structure with the total barotropic component equal to zero. Analytical considerations explaining this effect are presented and formulated in a more general statement which resembles but does not coincide with the "zero angular momentum theorem" of Flierl, Stern and Whitehead, 1983. In such steady translation the centroid of a bottom density anomaly is displaced horizon tally from the center of an upper-ocean vortex so the whole system moves due to this misalignment, which is known as a "he tonic mechanism". Cyclonic vortices go generally upslope, and anticyclones - in a downslope direction. The along-slope component of their motion depends upon the strength of a vortex, curvature of the bottom slope and background flows. When surrounded by a bowl-shaped topography anticyclonic vortices tend to stay near the deepest center of a basin, even resisting ambient flows which advect them outward. Application of this results to various oceanic examples (particularly to the "Shikmona eddy" in the Eastern Meditenanian) is discussed. Our results show that the behavior of a vortex over a sloping bottom differs significantly from its motion on the planetary beta-plane (but with a flat bottom). To explain this difference we introduce the concept of a "wave-breaking regime" relevant for the case of a planetary beta-effect, and a "wave-gliding regime" which characterizes the interaction of an eddy with a topographic slope.