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Something Old, Something New: Three Point Vortices on the Plane

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Abstract

The classic problem of three point vortex motion on the plane is revisited by using the interior angles of the vortex triangle, \(\theta_{j}\), \(j=1,2,3\), as the key system variables instead of the lengths of the triangle sides, \(s_{j}\), as has been used classically. Similar to the classic approach, the relative vortex motion can be represented in a phase space, with the topology of the level curves characterizing the motion. In contrast to the classic approach, the alternate formulation gives a compact, consistent phase space representation and facilitates comparisons of vortex motion in a co-moving frame. This alternate formulation is used to explore the vortex behavior in the two canonical cases of equal vortex strength magnitudes, \(\Gamma_{1}=\Gamma_{2}=\Gamma_{3}\) and \(\Gamma_{1}=\Gamma_{2}=-\Gamma_{3}\).

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Authors and Affiliations

  1. Department of Biomedical Engineering & Mechanics, Virginia Tech, VA 24061, Blacksburg, USA

    Mark A. Stremler

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  1. Mark A. Stremler
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Correspondence to Mark A. Stremler.

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MSC2010

01-02

37E35

70F07

70H06

76B47

76-03

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Stremler, M.A. Something Old, Something New: Three Point Vortices on the Plane. Regul. Chaot. Dyn. 26, 482–504 (2021). https://doi.org/10.1134/S1560354721050038

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  • DOI: https://doi.org/10.1134/S1560354721050038

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