Vortex dynamics in a shearing zonal flow

Abstract

When vortices are embedded in a shearing zonal flow their interactions are changed qualitatively. If the zonal flow's shear and the vortex's strength are of the same order and opposite sign, the vortex is pulled into a thin spiral, fragments, and is destroyed in a turn-around time. If the signs are the same, the vortex redistributes its vorticity so that its maximum value is at the centre, and its shape is determined by the ratio of its vorticity to the shear of the surrounding zonal flow. The dynamics depends crucially on the exchange between the self-energy of the vortices and the interaction energy of the zonal flow with the vortices. A numerical example that shows all of these effects is the breakup of a vortex layer: either a single large vortex is formed or successively smaller and more numerous thin filaments of vorticity are created. Two stable vortices are shown to merge if their initial separation in the cross-zonal direction is smaller than a critical distance which is approximately equal the vortices’ radii. The motions of large vortices are constrained by conservation laws, but when the zonal flow is filled with small-scale filaments of vorticity, the large vortices exchange energy with the filaments so that they are no longer constrained by these laws, and their dynamics become richer. Energy is shown to flow from the large vortices to the filaments, and this observation is used to predict the strength of boundary layers and the critical separation distance for vortex merging.