Mean Magnetic Field and Noise Cross-Correlation in Magnetohydrodynamic Turbulence: Results from a One-Dimensional Model

TL;DR

This paper uses a one-dimensional MHD turbulence model to show that the energy spectrum is unaffected by mean magnetic fields and that noise cross-correlations do not alter the fundamental equations, challenging previous claims.

Contribution

It demonstrates that the energy spectrum in MHD turbulence is independent of mean magnetic field and that noise cross-correlations do not modify the equations, clarifying misconceptions in prior literature.

Findings

Energy spectrum independent of mean magnetic field.

Noise cross-correlations do not change the equations.

Comments on scaling and multiscaling properties.

Abstract

We show that a recently proposed [J. Fleischer and P.H. Diamond, {\em Phys. Rev. E}{\bf 58}, R2709 (1998)] one-dimensional Burgers-like model for magnetohydrodynamics (MHD) is in effect identical to existing models for drifting lines and sedimenting lattices. We use the model to demonstrate, contrary to claims in the literature, that the energy spectrum of MHD turbulence should be independent of mean magnetic field and that cross-correlations between the noise sources for the velocity and magnetic fields cannot change the structure of the equations under renormalisation. We comment on the scaling and the multiscaling properties of the stochastically forced version of the model.