Existence of asymmetric Burgers vortices and their asymptotic behavior at large circulations
Preprint Series # 896 Maekawa, Yasunori Existence of asymmetric Burgers vortices and their asymptotic behavior at large circulations. (2008); AbstractThe asymmetric Burgers vortices are vortex solutions to the three dimensional stationary NavierStokes equations for viscous incompressible fluids in the presence of an asymmetric background straining flow. The asymmetry of the straining flow is expressed by a nonnegative parameter less than $1$. The Burgers vortices have been used as a model which expresses tubelike structures of concentrated vorticity fields in turbulence, and they are numerically well investigated especially in the case of large circulation numbers. However, their existence was proved mathematically only when either the asymmetry of the straining flow is not so strong or the circulation number is sufficiently small. In this paper we prove the existence of asymmetric Burgers vortices for all circulation numbers and each asymmetry parameter less than $1$. We also obtain their asymptotic expansion at large circulation numbers, which gives an explanation for a symmetrizing effect by a fast rotation.
