Sub-Grid-Scale Description of Turbulent Magnetic Reconnection in Magnetohydrodynamics

TL;DR

This study investigates how unresolved turbulence in magnetohydrodynamics can enhance magnetic reconnection rates in high Reynolds number plasmas, revealing turbulence's significant role in fast reconnection processes.

Contribution

The paper introduces a sub-grid turbulence model within MHD simulations to analyze its impact on magnetic reconnection, extending previous work and exploring resistivity and guide field effects.

Findings

Turbulence enhances reconnection speed at high Reynolds numbers.

Energy transfer from large to small scales increases with turbulence.

Reconnection becomes faster with larger Reynolds numbers, even with small turbulence amplitudes.

Abstract

Magnetic reconnection requires, at least locally, a non-ideal plasma response. In collisionless space and astrophysical plasmas, turbulence could permit this instead of the too rare binary collisions. We investigated the influence of turbulence on the reconnection rate in the framework of a single fluid compressible MHD approach. The goal is to find out, whether unresolved, sub-grid for MHD simulations, turbulence can enhance the reconnection process in high Reynolds number astrophysical plasma. We solve, simultaneously with the grid-scale MHD equations, evolution equations for the sub-grid turbulent energy and cross helicity according to Yokoi's model (Yokoi (2013)) where turbulence is self-generated and -sustained through the inhomogeneities of the mean fields. Simulations of Harris and force free sheets confirm the results of Higashimori et al. (2013) and new results are obtained about the dependence on resistivity for large Reynolds number as well as guide field effects. The amount of energy transferred from large to the small scales is enhanced in case of fast turbulent reconnection and energy spectra are used to interpret the obtained regime of reconnection controlled by the turbulence timescale $\tau_t$. The overall process is even faster for larger Reynolds numbers controlled by the background molecular resistivity $\eta$, as long as the initial level of turbulence is not too large. This implies that turbulence plays an important role on fast reconnection at situation of large Reynolds number while the amplitude of turbulence can still be small.