Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1898337 | Physica D: Nonlinear Phenomena | 2006 | 17 Pages |
Abstract
In this paper we establish rigorously that the family of Burgers vortices of the three-dimensional Navier–Stokes equation is stable for small Reynolds numbers. More precisely, we prove that any solution whose initial condition is a small perturbation of a Burgers vortex will converge toward another Burgers vortex as time goes to infinity, and we give an explicit formula for computing the change in the circulation number (which characterizes the limiting vortex completely.) Our result is not restricted to the axisymmetric Burgers vortices, which have a simple analytic expression, but it applies to the whole family of non-axisymmetric vortices which are produced by a general uniaxial strain.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Thierry Gallay, C. Eugene Wayne,