Scaling and anisotropy of magnetohydrodynamic turbulence in a strong mean magnetic field

TL;DR

This study investigates the anisotropic energy distribution in incompressible MHD turbulence with a strong mean magnetic field, revealing a universal scaling law independent of direction and field strength.

Contribution

It introduces a new analysis method for anisotropic spectral energy distribution in MHD turbulence, demonstrating a universal scaling law across different directions and magnetic field strengths.

Findings

The 3D spectrum follows a direction-independent functional form $F(k/k_d)$.

The spectral amplitude drops at a wavenumber $k_0$, marking the start of the inertial range.

Scaling properties are consistent across varying magnetic field strengths and flow resistivities.

Abstract

We present a new analysis of the anisotropic spectral energy distribution in incompressible magnetohydrodynamic (MHD) turbulence permeated by a strong mean magnetic field. The turbulent flow is generated by high-resolution pseudo-spectral direct numerical simulations with large-scale isotropic forcing. Examining the radial energy distribution for various angles $\theta$ with respect to $\mathbf{B}_0$ reveals a specific structure which remains hidden when not taking axial symmetry with respect to $B_0$ into account. For each direction, starting at the forced large-scales, the spectrum first exhibits an amplitude drop around a wavenumber $k_0$ which marks the start of a scaling range and goes on up to a dissipative wavenumber $k_d(\theta)$. The 3D spectrum for $k \ge k_0$ is described by a single $\theta$-independent functional form $F(k/k_d)$, the scaling law being the same in every direction. The previous properties still hold when increasing the mean field from $B_0=5$ up to $B_0=10 \ b_{rms}$, as well as when passing from resistive to ideal flows. We conjecture that at fixed $B_0$ the direction-independent scaling regime is reached when increasing the Reynolds number above a threshold which raises with increasing $B_0$. Below that threshold critically balanced turbulence is expected.