Decay of magnetohydrodynamic turbulence from power-law initial conditions

We derive relations for the decay of the kinetic and magnetic energies and the growth of the Taylor and integral scales in unforced, incompressible, homogeneous, and isotropic three-dimensional magnetohydrodynamic (3DMHD) turbulence with power-law initial energy spectra. We also derive bounds for the decay of the cross and magnetic helicities. We then present results from systematic numerical studies of such decay both within the context of a MHD shell model and direct numerical simulations of 3DMHD. We show explicitly that our results about the power-law decay of the energies hold for times t< t*, where t* is the time at which the integral scales become comparable to the system size. For t< t*, our numerical results are consistent with those predicted by the principle of "permanence of large eddies."