Dynamics of a pair of vortices in a rectangle

I. A. Kunin, F. Hussain, X. Zhou

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

The dynamics of a pair of point vortices of opposite signs in a rectangular domain is investigated in the whole range of energies. This simplest nonintegrable system reflects important features of different vortex flows: Bénard convection, Görtler vortices, flow in a cavity etc. In contrast to an approximate "cloud-in-cell" method that has been used for many vortices, the exact equations of motion for an arbitrary system of point vortices in a rectangle are derived and applied to the particular case of a pair of vortices. Patterns of periodic, quasiperiodic, chaotic and billiards-type motions are revealed for generic cases and two limiting cases: two close vortices (near-dipole) and a vortex close to the boundary. New criteria of ergodicity are introduced, and it is found that some chaotic motions are close to, in some sense, ergodic ones.

Original languageEnglish
Pages (from-to)1835-1844
Number of pages10
JournalInternational Journal of Engineering Science
Volume32
Issue number11
DOIs
StatePublished - Nov 1994

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