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Imbalanced Weak Magnetohydrodynamic Turbulence

Lithwick, Yoram and Goldreich, Peter (2003) Imbalanced Weak Magnetohydrodynamic Turbulence. Astrophysical Journal, 582 (2). pp. 1220-1240. ISSN 0004-637X. doi:10.1086/344676.

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Weak MHD turbulence consists of waves that propagate along magnetic field lines, in both directions. When two oppositely directed waves collide, they distort each other, without changing their respective energies. Each wave suffers many collisions before cascading; by contrast, in strong MHD turbulence, waves cascade on the same timescale at which they collide. "Imbalance" means that more energy is going in one direction than the other. In general, MHD turbulence is imbalanced. Yet imbalanced MHD cascades are not understood. For example, turbulence in the solar wind is observed to be imbalanced, so solar wind turbulence will not be understood until a theory of the imbalanced cascade is developed. We solve weak MHD turbulence that is imbalanced. Of crucial importance is that the energies going in both directions are forced to equalize at the dissipation scale. This "pinning" of the energy spectra was discovered by Grappin and coworkers. It affects the entire inertial range. Weak MHD turbulence is particularly interesting because perturbation theory is applicable. Hence, it can be described with a simple kinetic equation. Galtier and coworkers derived this kinetic equation. We present a simpler, more physical derivation, based on the picture of colliding wavepackets. In the process, we clarify the role of the zero-frequency mode. We also explain why Goldreich & Sridhar claimed that perturbation theory is inapplicable, and why this claim is wrong. (Our "weak" is equivalent to Goldreich & Sridhar's "intermediate.") We perform numerical simulations of the kinetic equation to verify our claims. We construct simplified model equations that illustrate the main effects. Finally, we show that a large magnetic Prandtl number does not have a significant effect, and that hyperviscosity leads to a pronounced bottleneck effect.

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Additional Information:© 2003 The American Astronomical Society. Received 2002 July 27; accepted 2002 September 10. Research reported in this paper was supported by NSF grant AST 00-98301.
Funding AgencyGrant Number
NSFAST 00-98301
Subject Keywords:MHD — turbulence
Issue or Number:2
Record Number:CaltechAUTHORS:20130225-092533716
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Official Citation:Imbalanced Weak Magnetohydrodynamic Turbulence Yoram Lithwick and Peter Goldreich 2003 ApJ 582 1220
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:37106
Deposited By: Tony Diaz
Deposited On:25 Feb 2013 21:19
Last Modified:09 Nov 2021 23:26

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