Evolving geometry of a vortex triangle

Vikas S. Krishnamurthy, Hassan Aref, and Mark A. Stremler
Phys. Rev. Fluids 3, 024702 – Published 23 February 2018

Abstract

The motion of three interacting point vortices in the plane can be thought of as the motion of three geometrical points endowed with a dynamics. This motion can therefore be reformulated in terms of dynamically evolving geometric quantities, viz., the circle that circumscribes the vortex triangle and the angles of the vortex triangle. In this study, we develop the equations of motion for the center, Z, and radius, R, of this circumcircle; and for the angles of the vortex triangle, A,B, and C; and for the triangle orientation given by φ1. The equations of motion for R,A,B, and C form an autonomous dynamical system. A number of known results in the three-vortex problem follow readily from the equations, giving an alternate geometrical perspective on the problem.

  • Figure
  • Figure
  • Received 25 May 2017

DOI:https://doi.org/10.1103/PhysRevFluids.3.024702

©2018 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Vikas S. Krishnamurthy*

  • Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, Brazil

Hassan Aref

  • Department of Engineering Science and Mechanics, Virginia Tech, Blacksburg, Virginia 24061, USA

Mark A. Stremler

  • Department of Biomedical Engineering and Mechanics, Virginia Tech, Blacksburg, Virginia 24061, USA

  • *vikas.krishnamurthy2@gmail.com
  • Deceased.

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Vol. 3, Iss. 2 — February 2018

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