Existence and Stability of Asymmetric Burgers Vortices |
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Authors: | Thierry Gallay C Eugene Wayne |
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Institution: | (1) Institut Fourier, Université de Grenoble I, BP 74, 38402 Saint-Martin-d’Hères, France;(2) Department of Mathematics and Center for BioDynamics, Boston University, 111 Cummington St., Boston, MA 02215, USA |
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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 11]. We also show that
the asymmetric vortices are stable with respect to localized two-dimensional perturbations. |
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Keywords: | 76D05 76D17 35Q30 76Exx |
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