On the ellipticity of isolated anticyclonic eddies

Abstract

A simplified two-layer model is considered in order to describe the behavior of anticyclonic lens-like eddies embedded in a horizontally sheared flow. Attention is focused on light eddies (such as warm-core gulf stream rings) embedded in an infinitely deep fluid whose speed varies linearly in the horizontal direction. Non-linear solutions are constructed analytically using a power series expansion.

It is found that a lens-like eddy embedded in a horizontally sheared flow, on an f plane, migrates at the average speed of the mean flow. As a result of the shear, the ring's shape is an ellipsoid whose orientation depends on the environmental flow. When the environmental shear is cyclonic, the ellipse is oriented perpendicular to the mean flow, and when the environmental shear is anticyclonic, the ellipse orientation is parallel to the mean flow. Although the ring migrates at a speed which differs from the speed of most of the surrounding fluid, the elliptical shape is fixed so that the whole eddy does not rotate due to the shear.

A possible application of this theory to the warm-core rings found north of the gulf stream is discussed.