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

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 $\mathrm{P}{\mathrm{r}}_{\mathrm{M}}$ over a large range, namely, $0.01\le \mathrm{P}{\mathrm{r}}_{\mathrm{M}}\le 10$. 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 $\mathrm{P}{\mathrm{r}}_{\mathrm{M}}$, to smaller intermittency in the magnetic field than in the velocity field, at low $\mathrm{P}{\mathrm{r}}_{\mathrm{M}}$. 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 $\mathrm{P}{\mathrm{r}}_{\mathrm{M}}$, multiscaling exponent ratios agree, at least within our errorbars, for both decaying and statistically steady homogeneous, isotropic MHD turbulence.

49 pages,33 figures

References in corpus (17)

• Generation of magnetic field by dynamo action in a turbulent flow of liquid sodium
• Simulations of nonhelical hydromagnetic turbulence
• Numerical demonstration of fluctuation dynamo at low magnetic Prandtl numbers
• Strong Anisotropic MHD Turbulence with Cross Helicity
• Rapid directional alignment of velocity and magnetic field in magnetohydrodynamic turbulence
• Small scale structures in three-dimensional magnetohydrodynamic turbulence
• Numerical Measurements of the Spectrum in Magnetohydrodynamic Turbulence
• Sub-Kolmogorov-Scale Fluctuations in Fluid Turbulence
• Energy spectra stemming from interactions of Alfven waves and turbulent eddies
• Dynamic Alignment and Exact Scaling Laws in MHD Turbulence
• Spectral Modeling of Turbulent Flows and the Role of Helicity
• Subcritical dynamo bifurcation in the Taylor Green flow
• Multi-scale model of gradient evolution in turbulent flows
• Energy decay laws in strongly anisotropic MHD turbulence
• Spectral Modeling of Magnetohydrodynamic Turbulent Flows
• Simulations of the anisotropic kinetic and magnetic alpha effects
• Scaling laws of turbulent dynamos

Cited by in corpus (8)

• Magnetic Prandtl number dependence of kinetic to magnetic dissipation ratio
• Lagrangian Statistics for Navier-Stokes Turbulence under Fourier-mode reduction: Fractal and Homogeneous Decimations
• 3D Simulations of Oxygen Shell Burning with and without Magnetic Fields
• Reynolds-number dependence of the dimensionless dissipation rate in homogeneous magnetohydrodynamic turbulence
• Examination of the four-fifths law for longitudinal third-order moments in incompressible magnetohydrodynamic turbulence in a periodic box
• Statistics of the inverse-cascade regime in two-dimensional magnetohydrodynamic turbulence
• Two-dimensional magnetohydrodynamic turbulence with large and small energy-injection length scales
• The statistical properties of spiral- and scroll-wave turbulence in cardiac tissue