  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.
