Localized instabilities of vortex rings with swirl

Alexander Lifschitz, Eliezer Hameiri

Research output: Contribution to journalArticle

Abstract

Axisymmetric vortex rings with swirl in an inviscid incompressible fluid are considered and it is demonstrated how the geometrical optics method can be used for investigating their stability. The evolution of rapidly oscillating initial data is studied and it is shown that the corresponding rings are unstable if the transport equations associated with the wave which is advected by the flow have unbounded solutions. It is shown that unbounded solutions grow either exponentially or algebraically. By means of the analysis of the corresponding transport equations effective stability conditions for general vortex rings with swirl are obtained. © 1993 John Wiley & Sons, Inc.

Original languageEnglish (US)
Pages (from-to)1379-1408
Number of pages30
JournalCommunications on Pure and Applied Mathematics
Volume46
Issue number10
DOIs
StatePublished - Nov 1993

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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