Evolution of anisotropic structures and turbulence in the multidimensional Burgers equation

Abstract

The goal of the present paper is the investigation of the final evolution of anisotropic regular structures and turbulence at large Reynolds number in the multidimensional Burgers equation. We show that we have local isotropization at small scales of the velocity and potential fields inside cellular zones. For periodic waves, we have simple decay inside a frozen structure. The global structure at large times is determined by the initial correlations and for short range correlated fields we have isotropization of turbulence. Finally, we consider the final behavior of the field, when the processes of nonlinear beating interactions become frozen, and the evolution of the field is determined only by the linear dissipation.