The Decay of Magnetohydrodynamic Turbulence from Power-Law Initial Conditions

TL;DR

This paper develops theoretical relations and provides numerical evidence for the decay behavior of kinetic and magnetic energies in magnetohydrodynamic turbulence with power-law initial conditions, highlighting the role of large-scale structures.

Contribution

It introduces new theoretical bounds and numerical validation for the decay laws of MHD turbulence starting from power-law spectra, extending understanding of turbulence evolution.

Findings

Energy decay follows power-law behavior before the integral scales reach system size.

Numerical results align with the principle of permanence of large eddies.

Decay laws are valid for times t < t_* where t_* marks the scale-system size crossover.

Abstract

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 an MHD shell model and direct numerical simulations (DNS) 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'.