Anisotropic MHD turbulence

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-Alfven waves propagating parallel to a large-scale magnetic field, as well as direct simulations demonstrate rigorously an anisotropic energy spectrum that scales as k(perpendicular to)(-2). 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].