Existence and stability of asymmetric Burgers vortices

Details Existence and stability of asymmetric Burgers vortices Existence and stability of asymmetric Burgers vortices

2005-03-17

arxiv.org/abs/math/0503353v1

Mathematics

Analysis of PDEs

17 pages, no figure

Scientific paper

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 and Ohkitani (1994). We also show that the asymmetric vortices are stable with respect to localized two-dimensional perturbations.

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