Exact Relation with Two-point Correlation Functions and Phenomenological Approach for Compressible Magnetohydrodynamic Turbulence

TL;DR

This paper derives an exact relation for two-point correlation functions in compressible MHD turbulence, revealing magnetic field effects and proposing a phenomenological model for energy spectra.

Contribution

It generalizes the Kolmogorov relation to compressible MHD turbulence, incorporating magnetic effects and providing a simplified phenomenology for energy spectra.

Findings

Magnetic field introduces new source and flux terms.

Exact relation generalizes hydrodynamic results.

Proposed axisymmetric energy spectra prediction.

Abstract

Compressible isothermal magnetohydrodynamic turbulence is analyzed under the assumption of statistical homogeneity and in the asymptotic limit of large kinetic and magnetic Reynolds numbers. Following Kolmogorov we derive an exact relation for some two-point correlation functions which generalizes the expression recently found for hydrodynamics. We show that the magnetic field brings new source and flux terms into the dynamics which may act on the inertial range similarly as a source or a sink for the mean energy transfer rate. The introduction of a uniform magnetic field simplifies significantly the exact relation for which a simple phenomenology may be given. A prediction for axisymmetric energy spectra is eventually proposed.