Spectral energy dynamics in magnetohydrodynamic turbulence

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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, Eₖʳ=|Eₖᵐ-Eₖᵏ|, and total energy, Eₖ=Eᵏₖ+Eᵐₖ, are observed to scale self-similarly in the inertial range as Eₖʳ k⁻⁷/³, Eₖ k⁻⁵/³ (isotropic case) and Eʳₖ⊥ k⊥⁻², Eₖ⊥ 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 Eₖʳ k E²ₖ which is confirmed by the simulations.