Scaling and anisotropy of magnetohydrodynamic turbulence in a strong mean magnetic field

Roland Grappin; Wolf-Christian Müller

doi:10.1103/PhysRevE.82.026406

paper

Scaling and anisotropy of magnetohydrodynamic turbulence in a strong mean magnetic field

arXiv:1008.0727 · doi:10.1103/PhysRevE.82.026406

Abstract

We present a new analysis of the anisotropic spectral energy distribution in incompressible magnetohydrodynamic (MHD) turbulence permeated by a strong mean magnetic field. The turbulent flow is generated by high-resolution pseudo-spectral direct numerical simulations with large-scale isotropic forcing. Examining the radial energy distribution for various angles $θ$ with respect to $B_{0}$ reveals a specific structure which remains hidden when not taking axial symmetry with respect to $B_{0}$ into account. For each direction, starting at the forced large-scales, the spectrum first exhibits an amplitude drop around a wavenumber $k_{0}$ which marks the start of a scaling range and goes on up to a dissipative wavenumber $k_{d} (θ)$ . The 3D spectrum for $k \geq k_{0}$ is described by a single $θ$ -independent functional form $F (k / k_{d})$ , the scaling law being the same in every direction. The previous properties still hold when increasing the mean field from $B_{0} = 5$ up to $B_{0} = 10 b_{r m s}$ , as well as when passing from resistive to ideal flows. We conjecture that at fixed $B_{0}$ the direction-independent scaling regime is reached when increasing the Reynolds number above a threshold which raises with increasing $B_{0}$ . Below that threshold critically balanced turbulence is expected.

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Scaling and anisotropy of magnetohydrodynamic turbulence in a strong mean magnetic field

Abstract

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