Incompressible MHD Turbulence

  • Peter Goldreich


The inertial range of incompressible MHD turbulence is most conveniently describedin terms of counter propagating waves. Shear Alfvén waves control the cascade dynamics. Slowwaves play a passive role and adopt the spectrum set by the shear Alfvén waves. Cascades composedentirely of shear Alfvén waves do not generate a significant measure of slow waves. MHD turbulenceis anisotropic with energy cascading more rapidly along k⊥. than along k∥. Anisotropy increases withk⊥. such that the excited modes are confined inside a cone bounded by k∥ α k2/3. The opening angleof the cone, θ(k⊥) α k- 1/3, defines the scale dependent anisotropy. MHD turbulence is genericallystrong in the sense that the waves which comprise it are critically damped. Nevertheless, deep insidethe inertial range, turbulent fluctuations are small. Their energy density is less than that of thebackground field by a factor θ2(k⊥) << 1. MHD cascades are best understood geometrically. Wavepackets suffer distortions as they move along magnetic field lines perturbed by counter propagatingwave packets. Field lines perturbed by unidirectional waves map planes perpendicular to the localfield into each other. Shear Alfvén waves are responsible for the mapping’s shear and slow waves forits dilatation. The former exceeds the latter by θ- 1 (k⊥) >> 1 which accounts for dominance of theshear Alfvén waves in controlling the cascade dynamics.


MHD, Turbulence 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Goldreich P. and Sridhar S.: 1995, Toward a Theory of Interstellar Turbulence. II. Strong Alfvénic Turbulence, Astrophys. J. 438, 763–775.ADSCrossRefGoogle Scholar
  2. Goldreich P. and Sridhar S.: 1997, Magnetohydrodynamic Turbulence Revisited, Astrophys. J. 485, 680–688.ADSCrossRefGoogle Scholar
  3. Iroshnikov, P.S.: 1963, Turbulence of a Conducting Fluid in a Strong Magnetic Field, Astronomicheskii Zhurnal 40, 742–750.ADSGoogle Scholar
  4. Kraichnan, R.H.: 1965, Inertial Range Spectrum of Hydromagnetic Turbulence, Physics of Fluids 8, 1385–1387.MathSciNetADSCrossRefGoogle Scholar
  5. Ng, C.S. and Bhattacharjee, A.: 1996, Interaction of Shear-Alfven Wave Packets: Implication for Weak Magnetohydrodynamic Turbulence in Astrophysical Plasmas, Astrophys. J. 465, 845–854.ADSCrossRefGoogle Scholar
  6. Shebalin, J.V., Matthaeus, w.H. and Montgomery, D.: 1983, Anisotropy in MHD Turbulence Due to a Mean Magnetic Field, J. Plasma Phys. 29, 525–547.ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Peter Goldreich
    • 1
  1. 1.California Institute of TechnologyPasadenaUSA

Personalised recommendations