Relative equilibrium and collapse configurations of heterogeneous vortex triple rings

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,...

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Bibliographic Details
Published in:Physica. D 2007-12, Vol.236 (2), p.123-130
Main Author: O’Neil, Kevin A.
Format: Article
Language:English
Subjects:
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Exact sciences and technology
Physics
Point vortex
Relative equilibrium
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Summary: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.
ISSN:0167-2789
1872-8022
DOI:10.1016/j.physd.2007.07.015