Chapter

MHD Turbulence: Scaling Laws and Astrophysical Implications

DOI: 10.1007/3-540-36238-X_3

ABSTRACT Turbulence is the most common state of astrophysical flows. In typical astrophysical fluids, turbulence is accompanied by
strong magnetic fields, which has a large impact on the dynamics of the turbulent cascade. Recently, there has been a significant
breakthrough on the theory of magnetohydrodynamic (MHD) turbulence. For the first time we have a scaling model that is supported
by both observations and numerical simulations. We review recent progress in studies of both incompressible and compressible
turbulence. We compare Iroshnikov-Kraichnan and Goldreich-Sridhar models, and discuss scalings of Alfvén, slow, and fast waves.
We also discuss the completely new regime of MHD turbulence that happens below the scale at which hydrodynamic turbulent motions
are damped by viscosity. In the case of the partially ionized diffuse interstellar gas the viscosity is due to neutrals and
truncates the turbulent cascade at ~parsec scales. We show that below this scale magnetic fluctuations with a shallow spectrum
persist and discuss the possibility of a resumption of the MHD cascade after ions and neutrals decouple. We discuss the implications
of this new insight into MHD turbulence for cosmic ray transport, grain dynamics, etc., and how to test theoretical predictions
against observations.

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