_ Vol. 26 (1) (2000) pp. 13-33 _
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Fluid Dynamics Research, Vol. 26 (1) (2000) pp. 13-33
© 2000 Elsevier Science B.V. All rights reserved.
PII: S0169-5983(99)00014-3

Evolution of a Lamb quadrupolar vortex

O.U. Velasco Fuentes * ovelasco@cicese.mx

Departamento de Oceanograf} F進ca, CICESE, Ensenada, BC, Mexico

Received 24 August 1998; received in revised form 24 February 1999; accepted 6 March 1999

Abstract

The Lamb vortices are stationary solutions of the Euler equations in two dimensions. The well-known dipolar vortex is the simplest of these structures; the quadrupolar vortex, formed by four counter rotating vortices within a circular region and a linear strain flow in the exterior, is second in increasing order of complexity. Here the evolution of a perturbed Lamb quadrupolar vortex is studied numerically. It is found that the vortex survives as a quadrupolar structure when the perturbed structure preserves the reflection symmetry with respect to each strain axis. In contrast, the vortex either survives or is destroyed when the perturbed state preserves only one reflection symmetry, depending on which axis remains as a symmetry line. Finally, the vortex is always destroyed when the perturbed state loses the two reflection symmetries of the original quadrupole.

Keywords: Two-dimensional vortices; Euler equations; Quadrupole; Dipole; Monopole; Stability

*Corresponding author address: CICESE, P.O. Box 434844, San Diego, CA 92143, USA. Telephone: +52-61-745050; Fax: +52-61-750547

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