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Self-similar vortex configurations: Collapse, expansion, and rigid-vortex motion

Sreethin Sreedharan Kallyadan* and Priyanka Shukla†

  • Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India

  • *sreethin2@gmail.com
  • †priyanka@iitm.ac.in
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Phys. Rev. Fluids 7, 114701 – Published 28 November, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.114701

Abstract

The problem of finding initial conditions that lead to self-similar motion of point vortices is formulated as a linear system. The linearity in the equations is used to check for the existence of similarity solutions with a given shape and, in particular, to numerically find self-similar vortex configurations with or without any prior knowledge of circulations. Algorithms for computing the one-parameter family of collapse and expansion configurations and the finitely many rigid-vortex configurations present in the family are also discussed. Typical families are shown to have vortices parametrized along closed curves, and the conditions for which they are not closed are investigated via several numerical examples.

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Outline

Information

Phys. Rev. Fluids 7, 114701– Published 28 November, 2022
  • Received 6 June 2022
  • Accepted 2 November 2022
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