Energy decay laws in strongly anisotropic MHD turbulence

TL;DR

This paper studies how a strong uniform magnetic field affects energy decay in incompressible MHD turbulence, revealing anisotropic decay laws and validating predictions through numerical simulations.

Contribution

It introduces a phenomenological model accounting for anisotropic energy transfer in MHD turbulence under strong magnetic fields, predicting distinct decay laws for different wave modes.

Findings

Energy decay slows down with increasing magnetic field strength.

Distinct power laws for shear- and pseudo-Alfvén wave energy decay.

Numerical simulations support the predicted anisotropic decay behavior.

Abstract

We investigate the influence of a uniform magnetic field ${\bf B_0}=B_0 e//$ on energy decay laws in incompressible magnetohydrodynamic (MHD) turbulence. The nonlinear transfer reduction along $B_0$ is included in a model that distinguishes parallel and perpendicular directions, following a phenomenology {\it \`a la} Kraichnan. We predict a slowing down of the energy decay due to anisotropy in the limit of strong $B_0$, with distinct power laws for energy decay of shear- and pseudo-Alfv\'en waves. Numerical results from the kinetic equations of Alfv\'en wave turbulence recover these predictions, and MHD numerical results clearly tend to follow them in the lowest perpendicular planes.