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An Exact Relation For Compressible MHD Turbulence

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Compressible isothermal magnetohydrodynamic turbulence is discussed under the assumption of statistical homogeneity and in the asymptotic limit of large kinetic and magnetic Reynolds numbers. Following Kolmogorov, under the above context, we have de- rived an exact relation for some two-point correlation functions which generalizes our previous work for compressible hydrodynamics. We show that the magnetic field brings new source and flux terms into the dynamics. The introduction of a strong and uniform magnetic field simplifies significantly the exact relation for which a simple phenomenology is proposed. A prediction for axisymmetric energy spectra is also discussed. The principal domain of application of our theoretical work is the interstellar medium which is observed to be turbulent, magnetized and supersonic.

Author(s):

Supratik BANERJEE    
Institut d'Astrophysique Spatiale (IAS), Bât. 121, Campus Univ. Paris-Sud, 91405, Orsay
France

Sébastien GALTIER    
Institut d'Astrophysique Spatiale (IAS), Bât. 121, Campus Univ. Paris-Sud, 91405, Orsay
France