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A survey of the stability criteria of Thomson’s vortex polygons outside a circular domain

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Abstract

The model of point vortices located outside a circular domain is considered. The review of stability and instability conditions of a system of identical point vortices located uniformly on a circle is given. Theoretical results are confirmed by numerical calculations.

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Acknowledgments

This research is supported by the Ministry of Education and Science of the Russian Federation, Southern Federal University (Project No. 1.1398.2014/K). The authors are grateful to M. Yu. Zhukov for valuable discussions.

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Authors and Affiliations

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

    Leonid Kurakin, Andrey Melekhov & Irina Ostrovskaya

  2. Southern Mathematical Institute VSC RAS, Vladikavkaz, Russia

    Leonid Kurakin

Authors
  1. Leonid Kurakin
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  2. Andrey Melekhov
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  3. Irina Ostrovskaya
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Correspondence to Leonid Kurakin.

Additional information

To Sergey Grudsky on the occasion of his 60th birthday.

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Kurakin, L., Melekhov, A. & Ostrovskaya, I. A survey of the stability criteria of Thomson’s vortex polygons outside a circular domain. Bol. Soc. Mat. Mex. 22, 733–744 (2016). https://doi.org/10.1007/s40590-016-0121-y

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  • DOI: https://doi.org/10.1007/s40590-016-0121-y

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