On a linearized operator of the equation for Burgers vortices
Preprint Series # 841 Maekawa, Yasunori On a linearized operator of the equation for Burgers vortices. (2007); AbstractBurgers vortices have been used as a model which expresses concentrated vorticity fields in turbulence. Several numerical results indicate that as the vortex Reynolds number is increasing, the associated Burgers vortex becomes more radial symmetric and has simpler structures. The purpose of this paper is to give a mathematical explanation for these numerical observations by studying a linearized operator of the equation for Burgers vortices. Based on the previous works by Th. Gallay and C. E. Wayne, we obtain some estimates and spectrum behavior of the linearized operator at large Reynolds numbers which are compatible with the numerical observations.
