Three-dimensional stability of elliptical vortex columns in external strain flows

B. J. Bayly, D. D. Holm, A. Lifschitz

Research output: Contribution to journalArticlepeer-review

60 Scopus citations


The Kirchhoff-Kida family of elliptical vortex columns in flows with uniform strain and rotation displays a rich variety of dynamical behaviours, even in a purely two-dimensional setting. In this paper, we address the stability of these columns with respect to three-dimensional perturbations via the geometrical optics method. In the case when the external strain is equal to zero, the analysis reduces to the stability of a steady elliptical vortex in a rotating frame. When the external strain is non-zero, the stability analysis reduces to the theory of a Schrödinger equation with quasi-periodic potential. We present stability results for a variety of different Kirchhoff-Kida flows. The vortex columns are typically unstable except when the interior vorticity is approximately the negative of the background vorticity, so that the flow in the inertial frame is nearly a potential flow.

Original languageEnglish (US)
Pages (from-to)895-926
Number of pages32
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number1709
StatePublished - Apr 15 1996

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering
  • General Physics and Astronomy


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