Spectral Energy Dynamics in Magnetohydrodynamic Turbulence

Spectral direct numerical simulations of incompressible MHD turbulence at a resolution of up to 10243 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, Ek^R=|E_k^{M-E_k^{K}|, and total energy, E_k=E^{K}_k+E^{M}_k, are observed to scale self-similarly in the inertial range as E_k^{R}~ k^{-7/3}, E_k~ k^{-5/3} (isotropic case) and E^{R}k_\perp~ k_\perp-2, Ek_\perp~ k_\perp^{-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}~ k E2_k which is confirmed by the simulations.

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