Existence and stability of asymmetric Burgers vortices

Thierry Gallay (1) , C. Eugene Wayne (2)

1 IF - Institut Fourier
2 Department of Mathematics and Statistics [Boston]

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

Domaines: Equations aux dérivées partielles [math.AP]

Thierry Gallay, C. Eugene Wayne. Existence and stability of asymmetric Burgers vortices. Journal of Mathematical Fluid Mechanics, 2007, 9, pp.243-261. ⟨hal-00351482⟩