Orbiting eddies

In this brief note, exact nonlinear solutions for lens-like eddies (i.e. blobs of oceanic water with anomalous density and anomalous vorticity) orbitting in an inertial circle are derived. The governing equations are nonlinear (i.e. ageostrophic) because the Rossby number is of order unity and the amplitude is of the same order as the maximum depth. Inviscid solutions for zero potential vorticity lenses are derived by transforming the equations of motion to a coordinate system traveling with the eddies along a circular path. It is shown that the lenses drift counter-clockwise at a tangential speed of fr0, where f is the Coriolis parameter and r0 is the radius of the orbit. The structure of the orbiting lens is identical to that of a stationary lens or a westward drifting lens, namely, the radius of the orbiting lens is 2 equation image times the Rossby radius and the swirl speed (i.e. the speed at which the fluid spins within the lens) is −fr/2 (where r is the radius). It is suggested that actual lenses in the ocean might very well display such an oscillatory behaviour. However, high-frequency observations are necessary in order to identify these aspects.