Spectral Energy Dynamics in Magnetohydrodynamic Turbulence

Spectral direct numerical simulations of incompressible MHD turbulence at a resolution of up to 1024^3 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₊^R=|E₊^M-E₊^K|, and total energy, E₊=E₊^K+E₊^M, are observed to scale self-similarly in the inertial range as E₊^Rk^-7/3, E₊k^-5/3 (isotropic case) and E₊_{}^Rk_^-2, E₊_{}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 quasinormal Markovian closure approximation, explains the findings. The assumed interplay of turbulent dynamo and Alfv\'en effect yields E₊^RE₊^2, which is confirmed by the simulations.