Quasi-isotropic cascade in MHD turbulence with mean field

TL;DR

This paper develops a phenomenological model of incompressible MHD turbulence with a strong mean magnetic field, linking anisotropic models and predicting an isotropic energy spectrum with specific directional extents.

Contribution

It introduces a quasi-isotropic cascade model in MHD turbulence that connects strong and weak turbulence regimes and predicts a universal energy spectrum shape.

Findings

Energy spectrum has the same slope in all directions.

Inertial range extent ratio equals b_{rms}/B_0.

Model matches recent 3D MHD simulation results.

Abstract

We propose a phenomenological theory of incompressible magnetohydrodynamic turbulence in the presence of a strong large-scale magnetic field, which establishes a link between the known anisotropic models of strong and weak MHD turbulence We argue that the Iroshnikov-Kraichnan isotropic cascade develops naturally within the plane perpendicular to the mean field, while oblique-parallel cascades with weaker amplitudes can develop, triggered by the perpendicular cascade, with a reduced flux resulting from a quasi-resonance condition. The resulting energy spectrum $E(k_\parallel,k_\bot)$ has the same slope in all directions. The ratio between the extents of the inertial range in the parallel and perpendicular directions is equal to $b_{rms}/B_0$. These properties match those found in recent 3D MHD simulations with isotropic forcing reported in [R. Grappin and W.-C. M\"uller, Phys. Rev. E \textbf{82}, 26406 (2010)].