On spectral scaling laws for incompressible anisotropic magnetohydrodynamic turbulence

Abstract

A heuristic model is given for anisotropic magnetohydrodynamics turbulence in the presence of a uniform external magnetic field B0ê‖. The model is valid for both moderate and strong B0 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‖∝k⊥2∕3 between parallel and perpendicular wave numbers (with reference to B0ê‖) and to obtain for the total-energy spectrum E(k⊥,k‖)∼k⊥−αk‖−β the universal prediction, 3α+2β=7. In particular, with such a prediction, the weak Alfvén wave turbulence constant-flux solution is recovered and, for the first time, a possible explanation to its precursor found numerically by Galtier et al. [J. Plasma Phys. 63, 447 (2000)] is given.