Chaotic scattering of two identical point vortex pairs revisited

Laust Emil Hjerrild Tophøj, Hassan Aref

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Abstract

A new numerical exploration suggests that the motion of two vortex pairs, with constituent vortices all of the same absolute circulation, displays chaotic scattering regimes. The mechanisms leading to chaotic scattering are different from the “slingshot effect” identified by Price [Phys. Fluids A 5, 2479 (1993)] and occur in a different region of the four-vortex phase space. They may, in many cases, be understood by appealing to the solutions of the three-vortex problem obtained by merging two like-signed vortices into one of twice the strength and by assuming that the four-vortex problem has unstable periodic solutions similar to those seen in the thereby associated three-vortex problems. The integrals of motion, linear impulse and Hamiltonian are recast in a form appropriate for vortex pair scattering interactions that provides constraints on the parameters characterizing the outgoing vortex pairs in terms of the initial conditions. ©2008 American Institute of Physics
Original languageEnglish
JournalPhysics of Fluids
Volume20
Issue number9
Pages (from-to)093605
ISSN1070-6631
DOIs
Publication statusPublished - 2008

Bibliographical note

Copyright (2008) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.

Keywords

  • Vortex dynamics
  • Chaos in fluid dynamics
  • rotating fluids

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