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Stability of the Thomson vortex polygon with evenly many vortices outside a circular domain

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Abstract

We consider the stability problem for the stationary rotation of a regular point vortex n-gon lying outside a circular domain. After the article of Havelock (1931), the complete solution of the problem remains unclear in the case 2 ≤ n ≤ 6. We obtain the exhaustive results for evenly many vortices n = 2, 4, 6.

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Authors and Affiliations

  1. Southern Federal University, Rostov-on-Don, Russia

    L. G. Kurakin & I. V. Ostrovskaya

Authors
  1. L. G. Kurakin
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  2. I. V. Ostrovskaya
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Correspondence to L. G. Kurakin.

Additional information

Original Russian Text Copyright © 2010 Kurakin L. G. and Ostrovskaya I. V.

The authors were supported by the CRDF-RFBR (Grants RUM1-2943-RD-09 and 09-01-92504-IK), the Federal Agency for Science and Innovation of the Russian Federation (Contract No. 02.740.11.5189), and the Russian Foundation for Basic Research (Grants 08-01-00895 and 10-05-00646). The research is a part of Program 2.1.1/554 of the Russian Federal Agency for Education.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 3, pp. 584–598, May–June, 2010.

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Kurakin, L.G., Ostrovskaya, I.V. Stability of the Thomson vortex polygon with evenly many vortices outside a circular domain. Sib Math J 51, 463–474 (2010). https://doi.org/10.1007/s11202-010-0048-x

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