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

Abstract

We present the results of our detailed pseudospectral direct numerical\nsimulation (DNS) studies, with up to $1024^3$ collocation points, of\nincompressible, magnetohydrodynamic (MHD) turbulence in three dimensions,\nwithout a mean magnetic field. Our study concentrates on the dependence of\nvarious statistical properties of both decaying and statistically steady MHD\nturbulence on the magnetic Prandtl number ${\\rm Pr_M}$ over a large range,\nnamely, $0.01 \\leq {\\rm Pr_M} \\leq 10$. We obtain data for a wide variety of\nstatistical measures such as probability distribution functions (PDFs) of\nmoduli of the vorticity and current density, the energy dissipation rates, and\nvelocity and magnetic-field increments, energy and other spectra, velocity and\nmagnetic-field structure functions, which we use to characterise intermittency,\nisosurfaces of quantities such as the moduli of the vorticity and current, and\njoint PDFs such as those of fluid and magnetic dissipation rates. Our\nsystematic study uncovers interesting results that have not been noted\nhitherto. In particular, we find a crossover from larger intermittency in the\nmagnetic field than in the velocity field, at large ${\\rm Pr_M}$, to smaller\nintermittency in the magnetic field than in the velocity field, at low ${\\rm\nPr_M}$. Furthermore, a comparison of our results for decaying MHD turbulence\nand its forced, statistically steady analogue suggests that we have strong\nuniversality in the sense that, for a fixed value of ${\\rm Pr_M}$, multiscaling\nexponent ratios agree, at least within our errorbars, for both decaying and\nstatistically steady homogeneous, isotropic MHD turbulence.\n