Relative equilibrium and collapse configurations of heterogeneous vortex triple rings

Abstract

Configurations of point vortices in a 2D fluid that are placed at the vertices of concentric regular m -gons, i.e. point vortex rings, are considered. The number of configurations that rotate uniformly–relative equilibria–is shown to be finite in the case of three rings with arbitrary circulations, subject to a few circulation constraints. Similar finiteness results for collapse configurations of three rings are also obtained, and an effective computational method is described.