Interaction of two unequal corotating vortices

Abstract

Previous high-resolution contour dynamics calculations [Dritschel and Waugh, Phys. Fluids A4, 1737 (1992)] have shown that in two-dimensional inviscid flow the interaction of two unequal corotating vortices with uniform vorticity is not always associated with vortex growth and may lead to vortices smaller than the original vortices. In the present study, we investigate whether these results also hold for two-dimensional vortices with continuous vorticity distributions. Similar flow regimes are found as for uniform vorticity patches, but the variation of the flow regimes with the initial vortex radii and peak vorticities is more complicated and strongly dependent on the initial shape of the vorticity profile. It is found that the “halo” of low-value vorticity, which surrounds the cores of continuous vortices, significantly increases the critical distance at which the weaker vortex is destroyed. The halo also promotes the vortex cores to merge more efficiently, since it accounts for a substantial part of the loss of circulation into filaments. Simple transformation rules and merger criteria are derived for the inviscid interaction between two Gaussian vortices. The strong dependence of the flow regimes on the initial vorticity distribution partly explains why previous laboratory experiments in an electron plasma [Mitchell and Driscoll, Phys. Fluids8, 1828 (1996)] show complete merger of two unequal vortices in a range of parameter space where contour dynamics simulations with uniform vorticity patches predict partial merger or partial straining-out of the smaller vortex. It is shown that the measured times for complete merger are in reasonable agreement with inviscid dynamics when the vortices are very similar. For more distinct vortices the weaker vortex is often observed to be destroyed on a time scale much smaller than expected from inviscid numerical simulations. An explanation for this discrepancy is given by the combined effects of vortex stripping and viscousdiffusion, which leads to an enhanced erosion of the weaker vortex. These results are verified by laboratory experiments in a conventional (rotating) fluid.