On spectral scaling laws for incompressible anisotropic magnetohydrodynamic turbulence

A heuristic model is given for anisotropic magnetohydrodynamics turbulence in the presence of a uniform external magnetic field B(0)e(parallel to). The model is valid for both moderate and strong B-0 and is able to describe both the strong and weak wave turbulence regimes as well as the transition between them. The main ingredient of the model is the assumption of constant ratio at all scales between the linear wave period and the nonlinear turnover time scale. Contrary to the model of critical balance introduced by Goldreich and Sridhar [Astrophys. J. 438, 763 (1995)], it is not assumed, in addition, that this ratio be equal to unity at all scales. This allows us to make use of the Iroshnikov-Kraichnan phenomenology; it is then possible to recover the widely observed anisotropic scaling law k(parallel to)proportional to k(perpendicular to)(2/3) between parallel and perpendicular wave numbers (with reference to B(0)e(parallel to)) and to obtain for the total-energy spectrum E(k(perpendicular to),k(parallel to))similar to k(perpendicular to)(-alpha)k(parallel to)(-beta) the universal prediction, 3 alpha+2 beta=7. In particular, with such a prediction, the weak Alfven wave turbulence constant-flux solution is recovered and, for the first time, a possible explanation to its precursor found numerically by Galtier [J. Plasma Phys. 63, 447 (2000)] is given. (C) 2005 American Institute of Physics.