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Azimuthal-mode solutions of two-dimensional Euler flows and the Chaplygin–Lamb dipole

  • A. Viúdez (a1)
Abstract

Exact solutions for multipolar azimuthal-mode vortices in two-dimensional Euler flows are presented. Flow solutions with non-vanishing far-field velocity are provided for any set of azimuthal wavenumbers $m$ and arbitrary number $n$ of vorticity shells. For azimuthal wavenumbers $m=0$ and $m=1$ , the far-field velocity is a rigid motion and unsteady flow solutions with vanishing far-field velocity are obtained by means of a time-dependent change of reference frame. Addition of these first two modes, in the case of $n=1$ , results in a particular Chaplygin–Lamb (C–L) dipole, with continuous and vanishing vorticity at the vortex boundary. Numerical simulations suggest that this particular C–L dipole is stable.

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Email address for correspondence: aviudez@cmima.csic.es
References
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Wayne, C. E. 2011 Vortices and two-dimensional fluid motion. Notices of the AMS 58, 1019.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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