Close pairs of relative equilibria for identical point vortices

Publication: Research - peer-reviewJournal article – Annual report year: 2011

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Numerical solution of the classical problem of relative equilibria for identical point vortices on the unbounded plane reveals configurations that are very close to the analytically known, centered, symmetrically arranged, nested equilateral triangles. New numerical solutions of this kind are found for 3n + 1 vortices, where n = 2, 3, ..., 30. A sufficient, although apparently not necessary, condition for this phenomenon of close solutions is that the "core" of the configuration is marginally stable, as occurs for a central vortex surrounded by an equilateral triangle. The open, regular heptagon also has this property, and new relative equilibria close to the nested, symmetrically arranged, regular heptagons have been found. The centered regular nonagon is also marginally stable. Again, a new family of close relative equilibria has been found. The closest relative equilibrium pairs occur, however, for symmetrically nested equilateral triangles. © 2011 American Institute of Physics.
Original languageEnglish
JournalPhysics of Fluids
Publication date2011
Volume23
Journal number5
Pages051706
ISSN1070-6631
DOIs
StatePublished

Bibliographical note

© 2011 American Institute of Physics

CitationsWeb of Science® Times Cited: 6
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