Unsteady behaviour of a topography-modulated tripole

The evolution of a tripolar vortex under the influence of a parabolic topography – like the free surface of a rotating fluid – is studied experimentally and with a point-vortex model. Laboratory experiments reveal that tripoles generated off-axis become asymmetric and the whole structure travels towards the centre of the tank along an anticyclonic spiral. During this translation the structure rotates quasi-periodically with the core pairing alternately with one of the satellites. An asymmetric point-vortex tripole (with the central vortex located at a distance [varepsilon] from the middle point of the configuration) displays a periodic motion which is qualitatively similar to the motion of the laboratory tripoles. The exchange of fluid between the three vortices as a function of the perturbation parameter [varepsilon] is studied using the lobe-dynamics technique. A point-vortex tripole modulated on the basis of conservation of potential vorticity reproduces quantitatively the trajectories of the individual vortices measured in the laboratory. As in the experiments, the model shows that fluid is strongly stirred in the region surrounding the vortex cores and that the tripole carries a finite amount of fluid