05-110 Thierry Gallay, C. Eugene Wayne
Existence and stability of asymmetric Burgers vortices (345K, Postscript) Mar 17, 05
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Abstract. Burgers vortices are stationary solutions of the three-dimensional Navier-Stokes equations in the presence of a background straining flow. These solutions are given by explicit formulas only when the strain is axisymmetric. In this paper we consider a weakly asymmetric strain and prove in that case that non-axisymmetric vortices exist for all values of the Reynolds number. In the limit of large Reynolds numbers, we recover the asymptotic results of Moffatt, Kida \& Ohkitani. We also show that the asymmetric vortices are stable with respect to localized two-dimensional perturbations.

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