The dynamics of a near-surface vortex are examined in a two-layer setting on the beta-plane. Initially, the vortex is radially symmetric and localized in the upper layer. Two non-dimensional parameters govern its evolution and translation: the ratio δ of the thickness of the vortex to the total depth of the fluid, and the non-dimensional beta-effect number α = βL/f (f and β are the Coriolis parameter and its meridional gradient respectively, L is the radius of the vortex). We assume, as suggested by oceanic observations, that α < δ < 1: A simple set of asymptotic equations is derived, which describes the beta-induced translation 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 features were observed: (i) The meridional (southward) component of the translation speed of the lens rapidly ‘overtakes’ the zonal (westward) component. The 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 different radii and amplitudes, follow the same trajectory. The amplitude and radius affect only the absolute value, but not the direction, of the translation speed. (iii) In the lower layer below the vortex, a ‘region’ is generated where the velocity of the fluid is growing linearly with time. The velocity field in the region becomes more and more homogeneous (and equal to the translation speed of the vortex).