On the existence of Burgers vortices for high Reynolds numbers

Axisymmetric or non-axisymmetric Burgers vortices have been studied numerically as a model of concentrated vorticity fields. Recently it has been rigorously proved that non-axisymmetric Burgers vortices exist for all values of the vortex Reynolds number if an asymmetry parameter is sufficiently small. On the other hand, several numerical results indicate that Burgers vortices have simpler structures as the vortex Reynolds number is increasing, even when the asymmetry parameter is not sufficiently small. In this paper we give a rigorous explanation for this numerical observation and extend the existence and stability results of Burgers vortices for high vortex Reynolds numbers.