On the Westward Translation of Isolated Eddies

Abstract

This paper examines the motion of an isolated lenslike eddy using the reduced-gravity shallow-water equations (SWE) on a ? plane. In contrast to previous studies the author uses a correct first-order ?-plane approximation of the SWE that posseses the same integrals of motion as the original system. The approximation includes terms proportional to (1 ? y tan?0/r0)?1, where y is the northward coordinate, ?0 the reference latitude, and r0 the earth?s mean radius. The center of mass of the eddy is found to oscillate meridionally and zonally with the inertial frequency f0 and drift westward at the same speed as in the case of the conventional ?-plane approximation. The new terms arising from the non-Cartesian metric cancel each other. Therefore, the ad hoc procedure of replacing f0 by f0 + ?y in the f-plane shallow-water equations does give the correct answer for the bulk motion of the eddy.