Anisotropic MHD Turbulence

TL;DR

This paper investigates anisotropic MHD turbulence, demonstrating that large-scale magnetic fields cause anisotropic energy spectra with specific scaling laws, supported by analytical, numerical, and observational evidence.

Contribution

It provides a comprehensive analysis of anisotropic MHD turbulence, highlighting the $k^{-2}_ot$ spectrum in the weak-turbulence limit and the development of anisotropy relative to local magnetic fields.

Findings

Anisotropic energy spectrum scales as $k^{-2}_ot$ in weak turbulence.

Anisotropy develops relative to local magnetic fields even without a background field.

Energy cascade rate aligns more with Iroshnikov-Kraichnan scaling than Kolmogorov.

Abstract

The solar wind and the interstellar medium are permeated by large-scale magnetic fields that render magnetohydrodynamic (MHD) turbulence anisotropic. In the weak-turbulence limit in which three-wave interactions dominate, analytical and high-resolution numerical results based on random scattering of shear-Alfv\'en waves propagating parallel to a large-scale magnetic field, as well as direct simulations demonstrate rigorously an anisotropic energy spectrum that scales as $k^{-2}_\perp$, instead of the famous Iroshnikov-Kraichnan (IK) spectrum of $k^{-3/2}$ for the isotropic case. Even in the absence of a background magnetic field, anisotropy is found to develop with respect to the local magnetic field, although the energy spectrum is globally isotropic and is found to be consistent with a $k^{-3/2}$ scaling. It is also found in direct numerical simulations that the energy cascade rate is much closer to IK scaling than a Kolmogorov scaling. Recent observations in the solar wind on cascade rates (as functions of the proton temperature and solar wind speed at 1 AU) seem to support this result [Vasquez et al. 2007].