## Close pairs of relative equilibria for identical point vortices

Publication: Research - peer-review › Journal article – Annual report year: 2011

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**Close pairs of relative equilibria for identical point vortices.** / Dirksen, Tobias; Aref, Hassan.

Publication: Research - peer-review › Journal article – Annual report year: 2011

### Harvard

*Physics of Fluids*, vol 23, no. 5, pp. 051706., 10.1063/1.3590740

### APA

*Physics of Fluids*,

*23*(5), 051706. 10.1063/1.3590740

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### MLA

*Physics of Fluids*. 2011, 23(5). 051706. Available: 10.1063/1.3590740

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### Bibtex

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TY - JOUR

T1 - Close pairs of relative equilibria for identical point vortices

AU - Dirksen,Tobias

AU - Aref,Hassan

PB - American Institute of Physics

N1 - © 2011 American Institute of Physics

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

U2 - 10.1063/1.3590740

DO - 10.1063/1.3590740

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 5

VL - 23

SP - 051706

ER -