The dynamics of a near-surface vortex in a two-layer ocean on the beta-plane

The dynamics of a near-surface vortex are examined in a two-layer setting o n the beta-plane. Initially, the vortex is radially symmetric and localized in the upper layer. Two non-dimensional parameters govern its evolution an d translation: the ratio delta of the thickness of the vortex to the total depth of the fluid, and the non-dimensional beta-effect number alpha = beta L/f (f and beta are the Coriolis parameter and its meridional gradient res pectively, L is the radius of the vortex). We assume, as suggested by ocean ic observations, that alpha much less than delta much less than 1. A simple set of asymptotic equations is derived, which describes the beta-induced t ranslation of the vortex and a dipolar perturbation developing on and under the vortex (in both layers). This set was solved numerically for oceanic lenses, and the following featu res were observed: (i) The meridional (southward) component of the translat ion speed of the lens rapidly 'overtakes' the zonal (westward) component. T he former grows approximately linearly, whereas the latter oscillates about the Nof (1981) value (i.e. about the speed of translation of a vortex in a one-layer reduce-gravity fluid). (ii) Vortices of the same shape, but diff erent radii and amplitudes, follow the same trajectory. The amplitude and r adius affect only the absolute value, but not the direction, of the transla tion speed. (iii) In the lower layer below the vortex, a 'region' is genera ted where the velocity of the fluid is growing linearly with time. The velo city held in the region becomes more and more homogeneous (and equal to the translation speed of the vortex).