A family of exact solutions of the Euler equations is presented: they are generalizations of the Kirchhoff vortex to N confocal ellipses. Special attention is given to the case N=2, for which the stability is analyzed with a method similar to the one used by Love [Proc. London Math. Soc. 1, XXV 18 (1893)] for the Kirchhoff vortex. The results are compared with those for the corresponding circular problem.
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Research Article| August 01 1986
Generalized Kirchhoff vortices
L. M. Polvani;
L. M. Polvani, G. R. Flierl; Generalized Kirchhoff vortices. Phys. Fluids 1 August 1986; 29 (8): 2376–2379. https://doi.org/10.1063/1.865530
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