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Exact relation with two-point correlation functions and phenomenological approach for compressible magnetohydrodynamic turbulence

TitleExact relation with two-point correlation functions and phenomenological approach for compressible magnetohydrodynamic turbulence
Publication TypeJournal Article
Year of Publication2013
AuthorsBanerjee, S, Galtier, S
JournalPhysical Review EPhysical Review E
Volume87
Pagination13019
Date PublishedJanuary 1, 2013
ISBN Number1063-651X
KeywordsCompressible flows, homogeneous turbulence, Isotropic turbulence, Magnetohydrodynamics, shock waves, Statistical theories and models
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.

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