Close pairs of relative equilibria for identical point vortices

dc.contributorVirginia Techen
dc.contributor.authorDirksen, T.en
dc.contributor.authorAref, Hassanen
dc.contributor.departmentBiomedical Engineering and Mechanicsen
dc.date.accessed2013-11-20en
dc.date.accessioned2013-12-04T14:59:21Zen
dc.date.available2013-12-04T14:59:21Zen
dc.date.issued2011-05-01en
dc.description.abstractNumerical 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. (C) 2011 American Institute of Physics.en
dc.description.sponsorshipDanish National Research Foundationen
dc.format.mimetypeapplication/pdfen
dc.identifier.citationDirksen, Tobias and Aref, Hassan, “Close pairs of relative equilibria for identical point vortices,” Phys. Fluids (1994-present), 23, 051706 (2011), DOI:http://dx.doi.org/10.1063/1.3590740en
dc.identifier.doihttps://doi.org/10.1063/1.3590740en
dc.identifier.issn1070-6631en
dc.identifier.urihttp://hdl.handle.net/10919/24393en
dc.identifier.urlhttp://scitation.aip.org/content/aip/journal/pof2/23/5/10.1063/1.3590740en
dc.language.isoen_USen
dc.publisherAmerican Institute of Physicsen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectRotating superfluiden
dc.subjectVortexen
dc.titleClose pairs of relative equilibria for identical point vorticesen
dc.title.serialPhysics of Fluidsen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten

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