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Imbalanced Strong MHD Turbulence

Lithwick, Y. and Goldreich, P. and Sridhar, S. (2007) Imbalanced Strong MHD Turbulence. Astrophysical Journal, 655 (1). pp. 269-274. ISSN 0004-637X. https://resolver.caltech.edu/CaltechAUTHORS:20130228-103329811

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Abstract

We present a phenomenological model of imbalanced MHD turbulence in an incompressible magnetofluid. The steady state cascades, of waves traveling in opposite directions along the mean magnetic field, carry unequal energy fluxes to small length scales, where they decay as a result of viscous and resistive dissipation. The inertial range scalings are well understood when both cascades are weak. We study the case in which both cascades are, in a sense, strong. The inertial range of this imbalanced cascade has the following properties: (1) The ratio of the rms Elsässer amplitudes is independent of scale and is equal to the ratio of the corresponding energy fluxes. (2) In common with the balanced strong cascade, the energy spectra of both Elsässer waves are of the anisotropic Kolmogorov form, with their parallel correlation lengths equal to each other on all scales, and proportional to the two-thirds power of the transverse correlation length. (3) The equality of cascade time and wave period (critical balance) that characterizes the strong balanced cascade does not apply to the Elsässer field with the larger amplitude. Instead, the more general criterion that always applies to both Elsässer fields is that the cascade time is equal to the correlation time of the straining imposed by oppositely directed waves. (4) In the limit of equal energy fluxes, the turbulence corresponds to the balanced strong cascade. Our results are particularly relevant for turbulence in the solar wind. Spacecraft measurements have established that in the inertial range of solar wind turbulence, waves traveling away from the Sun have higher amplitudes than those traveling toward it. Result 1 allows us to infer the turbulent flux ratios from the amplitude ratios, thus providing insight into the origin of the turbulence.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1086/509884DOIUNSPECIFIED
http://iopscience.iop.org/0004-637X/655/1/269/PublisherUNSPECIFIED
http://xxx.lanl.gov/abs/astro-ph/0607243arXivUNSPECIFIED
Additional Information:© 2007 The American Astronomical Society. Received 2006 July 17; accepted 2006 October 4.
Subject Keywords:MHD — turbulence
Issue or Number:1
Record Number:CaltechAUTHORS:20130228-103329811
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20130228-103329811
Official Citation:Imbalanced Strong MHD Turbulence Y. Lithwick et al. 2007 ApJ 655 269
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:37201
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:28 Feb 2013 20:21
Last Modified:03 Oct 2019 04:45

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