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dc.contributorVirginia Techen_US
dc.contributor.authorAref, Hassanen_US
dc.date.accessioned2013-12-04T14:59:20Z
dc.date.available2013-12-04T14:59:20Z
dc.date.issued2009-09-01
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_US
dc.identifier.issn1070-6631
dc.identifier.urihttp://hdl.handle.net/10919/24389
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_US
dc.description.sponsorshipDanish National Research Foundation
dc.format.mimetypeapplication/pdfen_US
dc.language.isoen_US
dc.publisherAmerican Institute of Physics
dc.subjectEigenvaluesen_US
dc.subjectEigenfunctionsen_US
dc.subjectFlow instabilityen_US
dc.subjectPattern formationen_US
dc.subjectVorticesen_US
dc.subjectZero total circulationen_US
dc.subjectRotating fluiden_US
dc.subject3-vortex motionen_US
dc.subjectVortexen_US
dc.titleStability of relative equilibria of three vorticesen_US
dc.typeArticle - Refereeden_US
dc.identifier.urlhttp://scitation.aip.org/content/aip/journal/pof2/21/9/10.1063/1.3216063
dc.date.accessed2013-11-20
dc.title.serialPhysics of Fluids
dc.identifier.doihttps://doi.org/10.1063/1.3216063
dc.type.dcmitypeTexten_US


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