Nonhelical turbulence and the inverse transfer of energy: A parameter study

TL;DR

This study investigates the inverse transfer of energy in nonhelical magnetohydrodynamical turbulence through a parameter study, revealing conditions for its occurrence and assessing its potential role in early universe magnetic field evolution.

Contribution

It provides a detailed parameter analysis of nonhelical inverse energy transfer, highlighting the conditions necessary for its occurrence and comparing its efficiency to helical turbulence.

Findings

Large Reynolds numbers ($a0 ext{O}(10^3)$) are required for inverse transfer.

Low Prandtl numbers ($Pr \,=\,1$) favor inverse transfer.

Inverse transfer is less efficient than inverse cascade in helical turbulence.

Abstract

We explore the phenomenon of the recently discovered inverse transfer of energy from small to large scales in decaying magnetohydrodynamical turbulence by Brandenburg et al. (2015) even for nonhelical magnetic fields. For this investigation we mainly employ the Pencil-Code performing a parameter study, where we vary the Prandtl number, the kinematic viscosity and the initial spectrum. We find that in order to get a decay which exhibits this inverse transfer, large Reynolds numbers ($\mathcal{O}\sim 10^{3}$) are needed and low Prandtl numbers of the order unity $Pr = 1$ are preferred. Compared to helical MHD turbulence, though, the inverse transfer is much less efficient in transferring magnetic energy to larger scales than the well-known effect of the inverse cascade. Hence, applying the inverse transfer to the magnetic field evolution in the Early Universe, we question whether the nonhelical inverse transfer is effective enough to explain the observed void magnetic fields if a magneto- genesis scenario during the electroweak phase transition is assumed.