Systematics of the magnetic-Prandtl-number dependence of homogeneous, isotropic magnetohydrodynamic turbulence

TL;DR

This study uses high-resolution numerical simulations to explore how the statistical properties of three-dimensional homogeneous isotropic MHD turbulence depend on the magnetic Prandtl number, revealing new insights into intermittency and universality.

Contribution

It provides the first detailed analysis of the Prandtl number dependence of various statistical measures in 3D MHD turbulence using high-resolution DNS.

Findings

Intermittency in magnetic and velocity fields varies with Pr_M.

Universality observed between decaying and steady turbulence at fixed Pr_M.

Identified crossover in intermittency behavior across Pr_M values.

Abstract

We present the results of our detailed pseudospectral direct numerical simulation (DNS) studies, with up to $1024^3$ collocation points, of incompressible, magnetohydrodynamic (MHD) turbulence in three dimensions, without a mean magnetic field. Our study concentrates on the dependence of various statistical properties of both decaying and statistically steady MHD turbulence on the magnetic Prandtl number ${\rm Pr_M}$ over a large range, namely, $0.01 \leq {\rm Pr_M} \leq 10$. We obtain data for a wide variety of statistical measures such as probability distribution functions (PDFs) of moduli of the vorticity and current density, the energy dissipation rates, and velocity and magnetic-field increments, energy and other spectra, velocity and magnetic-field structure functions, which we use to characterise intermittency, isosurfaces of quantities such as the moduli of the vorticity and current, and joint PDFs such as those of fluid and magnetic dissipation rates. Our systematic study uncovers interesting results that have not been noted hitherto. In particular, we find a crossover from larger intermittency in the magnetic field than in the velocity field, at large ${\rm Pr_M}$, to smaller intermittency in the magnetic field than in the velocity field, at low ${\rm Pr_M}$. Furthermore, a comparison of our results for decaying MHD turbulence and its forced, statistically steady analogue suggests that we have strong universality in the sense that, for a fixed value of ${\rm Pr_M}$, multiscaling exponent ratios agree, at least within our errorbars, for both decaying and statistically steady homogeneous, isotropic MHD turbulence.