The nonlinear evolution of rotating configurations of uniform vorticity

David G. Dritschel*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

118 Citations (Scopus)

Abstract

The nonlinear evolution of perturbed equilibrium configurations of constant-vorticity vortices is calculated. To illustrate a variety of nonlinear behaviour, we consider the following relatively simple configurations: the corotating configurations of N vortices whose linear stability has been treated in a previous study; the elliptical vortex; and the annular vortex. Our calculations test for nonlinear stability as well as categorize the possible forms of stability and instability. The energy ideas announced in the previous study are found to greatly constrain vortex evolution. In particular, we show that two vortices and an elliptical vortex may evolve into each other, and that an annular vortex may break cleanly into five corotating vortices.

Original languageEnglish
Pages (from-to)157-182
Number of pages26
JournalJournal of Fluid Mechanics
Volume172
DOIs
Publication statusPublished - 1 Jan 1986

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