Evolution of Magnetic Fields in Freely Decaying Magnetohydrodynamic Turbulence

TL;DR

This paper analytically investigates how magnetic fields evolve in freely decaying magnetohydrodynamic turbulence, revealing different scaling laws for helical and non-helical fields over time.

Contribution

It provides an analytical solution for the evolution of magnetic fields in MHD turbulence, including the effects of helicity and initial spectral conditions.

Findings

Non-helical magnetic energy decays as t^{-2(1+p)/(3+p)}

Helical magnetic energy decays as (log t)^{1/3} t^{-2/3}

Correlation length grows as t^{2/(3+p)} for non-helical and t^{2/3} for helical fields

Abstract

We study the evolution of magnetic fields in freely decaying magnetohydrodynamic turbulence. By quasi-linearizing the Navier-Stokes equation, we solve analytically the induction equation in quasi-normal approximation. We find that, if the magnetic field is not helical, the magnetic energy and correlation length evolve in time respectively as E_B \propto t^{-2(1+p)/(3+p)} and \xi_B \propto t^{2/(3+p)}, where p is the index of initial power-law spectrum. In the helical case, the magnetic helicity is an almost conserved quantity and forces the magnetic energy and correlation length to scale as E_B \propto (log t)^{1/3} t^{-2/3} and \xi_B \propto (log t)^{-1/3} t^{2/3}.