dc.contributor Virginia Tech en_US dc.contributor.author Aref, Hassan en_US dc.date.accessioned 2013-12-04T14:59:20Z dc.date.available 2013-12-04T14:59:20Z dc.date.issued 2009-09-01 dc.identifier.citation Aref, Hassan, “Stability of relative equilibria of three vortices,” Phys. Fluids (1994-present), 21, 094101 (2009), DOI:http://dx.doi.org/10.1063/1.3216063 en_US dc.identifier.issn 1070-6631 dc.identifier.uri http://hdl.handle.net/10919/24389 dc.description.abstract Three 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.sponsorship Danish National Research Foundation dc.format.mimetype application/pdf en_US dc.language.iso en_US dc.publisher American Institute of Physics dc.subject Eigenvalues en_US dc.subject Eigenfunctions en_US dc.subject Flow instability en_US dc.subject Pattern formation en_US dc.subject Vortices en_US dc.subject Zero total circulation en_US dc.subject Rotating fluid en_US dc.subject 3-vortex motion en_US dc.subject Vortex en_US dc.title Stability of relative equilibria of three vortices en_US dc.type Article - Refereed en_US dc.identifier.url http://scitation.aip.org/content/aip/journal/pof2/21/9/10.1063/1.3216063 dc.date.accessed 2013-11-20 dc.title.serial Physics of Fluids dc.identifier.doi https://doi.org/10.1063/1.3216063 dc.type.dcmitype Text en_US
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