On the existence of Burgers vortices for high Reynolds numbers
Preprint Series # 846
Maekawa, Yasunori On the existence of Burgers vortices for high Reynolds numbers. (2007);
Axisymmetric or non-axisymmetric Burgers vortices have been studied numerically as a model of concentrated vorticity fields. Recently, Th. Gallay and C. E. Wayne rigorously proved that non-axisymmetric Burgers vortices exist for all values of the vortex Reynolds number if an asymmetric parameter is sufficiently small. Several numerical results suggest that Burgers vortices have simpler structures if the vortex Reynolds number is large, even when the asymmetric parameter is not small. In this paper, we give a rigorous explanation for this numerical observation and extend the existence results obtained by Th. Gallay and C. E. Wayne for high vortex Reynolds numbers.