Direct Numerical Simulations of Three-dimensional Magnetohydrodynamic Turbulence with Random, Power-law Forcing

TL;DR

This study uses direct numerical simulations to analyze the statistical properties of 3D magnetohydrodynamic turbulence with power-law forcing, comparing it to conventional turbulence and examining multiscaling exponents and probability distributions.

Contribution

It introduces a stochastic forcing method with a power-law spectrum in DNS of 3D MHD turbulence and compares its statistical properties to standard turbulence.

Findings

Exponent ratios match those of conventional MHD turbulence within error margins.

Power-law forcing affects the energy spectra and structure functions.

Statistical properties are consistent across different magnetic Prandtl numbers.

Abstract

We present pseudospectral direct-numerical-simulation (DNS) studies of the three-dimensional magnetohydrodynamic (MHD) equations (3DRFMHD) with a stochastic force that has zero mean and a variance $\sim k^{-3}$, where $k$ is the wavenumber, because 3DRFMHD is used in field-theoretic studies of the scaling of energy spectra in MHD turbulence. We obtain velocity and magnetic-field spectra and structure functions and, from these, the multiscaling exponent ratios $\zeta_p/\zeta_3$, by using the extended self similarity (ESS) procedure. These exponent ratios lie within error bars of their counterparts for conventional three-dimensional MHD turbulence (3DMHD). We then carry out a systematic comparison of the statistical properties of 3DMHD and 3DRFMHD turbulence by examining various probability distribution functions (PDFs), joint PDFs, and isosurfaces of of, e.g., the moduli of the vorticity and the current density for three magnetic Prandtl numbers ${\rm Pr_M} = 0.1,~1$, and $10$.