Incompressible MHD Turbulence |
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Authors: | Peter Goldreich |
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Institution: | (1) California Institute of Technology, 150-21, Pasadena, CA, 91125, USA E-mail |
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Abstract: | The inertial range of incompressible MHD turbulence is most conveniently described in terms of counter propagating waves.
Shear Alfvén waves control the cascade dynamics. Slow waves play a passive role and adopt the spectrum set by the shear Alfvén
waves. Cascades composed entirely of shear Alfvén waves do not generate a significant measure of slow waves. MHD turbulence
is anisotropic with energy cascading more rapidly along k
⊥ than along k
∥. Anisotropy increases with k
⊥ such that the excited modes are confined inside a cone bounded by k
∥∝ k
perp
2/3. The opening angle of the cone, θ(k
⊥)∝ k
⊥
-1/3, defines the scale dependent anisotropy. MHD turbulence is generically strong in the sense that the waves which comprise
it are critically damped. Nevertheless, deep inside the inertial range, turbulent fluctuations are small. Their energy density
is less than that of the background field by a factor θ2(k
⊥)≪. MHD cascades are best understood geometrically. Wave packets suffer distortions as they move along magnetic field lines
perturbed by counter propagating wave packets. Field lines perturbed by unidirectional waves map planes perpendicular to the
local field into each other. Shear Alfvén waves are responsible for the mapping's shear and slow waves for its dilatation.
The former exceeds the latter by θ-1(k
⊥)≫ 1 which accounts for dominance of the shear Alfvén waves in controlling the cascade dynamics.
This revised version was published online in July 2006 with corrections to the Cover Date. |
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Keywords: | MHD Turbulence |
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