2006/07/11 by Yoram Lithwick, Peter Goldreich, S. Sridhar · 12 citations
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Geomagnetism and Paleomagnetism Studies #Ionosphere and magnetosphere dynamics #Solar and Space Plasma Dynamics #astro-ph
paper · pdf · doi:10.1086/509884
published as Astrophys.J.655:269-274,2007
arxiv created 2006/07/11 · openalex publication_date 2007/01/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
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.