The evolution of anisotropic structures and turbulence in the multi-dimensional Burgers equation

TL;DR

This paper investigates how anisotropic structures and turbulence evolve in the multi-dimensional Burgers equation at high Reynolds numbers, revealing local isotropization and the influence of initial correlations on large-scale behavior.

Contribution

It provides new insights into the anisotropic evolution and turbulence decay in the multi-dimensional Burgers equation, highlighting the roles of initial conditions and linear dissipation.

Findings

Local isotropization occurs at small scales within cellular zones.

Turbulence isotropization depends on initial correlation properties.

Large-time behavior is governed by initial correlations and linear dissipation.

Abstract

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