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Stability of relative equilibria of three vortices

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dc.contributorVirginia Techen
dc.contributor.authorAref, Hassanen
dc.contributor.departmentBiomedical Engineering and Mechanicsen
dc.date.accessed2013-11-20en
dc.date.accessioned2013-12-04T14:59:20Zen
dc.date.available2013-12-04T14:59:20Zen
dc.date.issued2009-09-01en
dc.description.abstractThree point vortices on the unbounded plane have relative equilibria wherein the vortices either form an equilateral triangle or are collinear. While the stability analysis of the equilateral triangle configurations is straightforward, that of the collinear relative equilibria is considerably more involved. The only comprehensive analysis available in the literature, by Tavantzis and Ting [Phys. Fluids 31, 1392 (1988)], is not easy to follow nor is it very physically intuitive. The symmetry between the three vortices is lost in this analysis. A different analysis is given based on explicit formulas for the three eigenvalues determining the stability, including a new formula for the angular velocity of rotation of a collinear relative equilibrium. A graphical representation of the space of vortex circulations is introduced, and the resultants between various polynomials that enter the problem are used. This approach adds considerable transparency to the solution of the stability problem and provides more physical understanding. The main results are summarized in a diagram that gives both the stability and instability of the various collinear relative equilibria and their sense of rotation.en
dc.description.sponsorshipDanish National Research Foundationen
dc.format.mimetypeapplication/pdfen
dc.identifier.citationAref, Hassan, “Stability of relative equilibria of three vortices,” Phys. Fluids (1994-present), 21, 094101 (2009), DOI:http://dx.doi.org/10.1063/1.3216063en
dc.identifier.doihttps://doi.org/10.1063/1.3216063en
dc.identifier.issn1070-6631en
dc.identifier.urihttp://hdl.handle.net/10919/24389en
dc.identifier.urlhttp://scitation.aip.org/content/aip/journal/pof2/21/9/10.1063/1.3216063en
dc.language.isoen_USen
dc.publisherAmerican Institute of Physicsen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectEigenvaluesen
dc.subjectEigenfunctionsen
dc.subjectFlow instabilityen
dc.subjectPattern formationen
dc.subjectVorticesen
dc.subjectZero total circulationen
dc.subjectRotating fluiden
dc.subject3-vortex motionen
dc.subjectVortexen
dc.titleStability of relative equilibria of three vorticesen
dc.title.serialPhysics of Fluidsen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten

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