Universal properties of three-dimensional magnetohydrodynamic turbulence: Do Alfv\'en waves matter?

TL;DR

This paper investigates how Alfvén waves influence the universal properties of 3D MHD turbulence, revealing that energy spectra remain Kolmogorov-like and multiscaling deviations decrease with stronger magnetic fields.

Contribution

It provides a self-consistent mode-coupling analysis showing the persistence of Kolmogorov scaling and the impact of mean magnetic fields on multiscaling in 3D MHD turbulence.

Findings

Energy spectra follow $k^{-5/3}$ scaling even with magnetic fields.

Multiscaling deviations decrease as magnetic field strength increases.

Results align with numerical and observational data.

Abstract

We analyse the effects of the propagating Alfv\'en waves, arising due to non-zero mean magnetic fields, on the nonequilibrium steady states of three-dimensional (3d) homogeneous Magnetohydrodynamic (MHD) turbulence. In particular, the effects of Alfv\'en waves on the universal properties of 3dMHD turbulence are studied in a one-loop self-consistent mode-coupling approach. We calculate the kinetic- and magnetic energy-spectra. We find that {\em even} in the presence of a mean magnetic field the energy spectra are Kolmogorov-like, i.e., scale as $k^{-5/3}$ in the inertial range where $\bf k$ is a Fourier wavevector belonging to the inertial range. We also elucidate the multiscaling of the structure functions in a log-normal model by evaluating the relevant intermittency exponents, and our results suggest that the multiscaling deviations from the simple Kolmogorov scaling of the structure functions decrease with increasing strength of the mean magnetic field. Our results compare favourably with many existing numerical and observational results.