Spectral energy dynamics in magnetohydrodynamic turbulence

Wolf-Christian Mueller; Roland Grappin

doi:10.1103/PhysRevLett.95.114502

paper

Spectral energy dynamics in magnetohydrodynamic turbulence

arXiv:physics/0509019 · doi:10.1103/PhysRevLett.95.114502

Abstract

Spectral direct numerical simulations of incompressible MHD turbulence at a resolution of up to $102 4^{3}$ collocation points are presented for a statistically isotropic system as well as for a setup with an imposed strong mean magnetic field. The spectra of residual energy, $E_{k}^{R} = ∣ E_{k}^{M} - E_{k}^{K} ∣$ , and total energy, $E_{k} = E_{k}^{K} + E_{k}^{M}$ , are observed to scale self-similarly in the inertial range as $E_{k}^{R} \sim k^{- 7/3}$ , $E_{k} \sim k^{- 5/3}$ (isotropic case) and $E_{k_{⊥}}^{R} \sim k_{⊥}^{- 2}$ , $E_{k_{⊥}} \sim k_{⊥}^{- 3/2}$ (anisotropic case, perpendicular to the mean field direction). A model of dynamic equilibrium between kinetic and magnetic energy, based on the corresponding evolution equations of the eddy-damped quasi-normal Markovian (EDQNM) closure approximation, explains the findings. The assumed interplay of turbulent dynamo and Alfvén effect yields $E_{k}^{R} \sim k E_{k}^{2}$ which is confirmed by the simulations.

accepted for publication by PRL

Spectral energy dynamics in magnetohydrodynamic turbulence

Abstract

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