Effects of forcing mechanisms on the multiscale properties of magnetohydrodynamics

TL;DR

This study uses numerical simulations to analyze how different large-scale forcing mechanisms influence the multi-scale energy transfer processes in magnetohydrodynamics, revealing the complex interplay between velocity and magnetic fields.

Contribution

It introduces a detailed decomposition of energy fluxes in MHD under various forcing scenarios, highlighting the flux-loop balance and the role of heterochiral and homochiral interactions.

Findings

Magnetic forcing near a = 1 significantly depletes kinetic energy flux.

Flux-loop balance occurs between heterochiral and homochiral transfers.

Energy transfer direction reverses around a = 0.4.

Abstract

We performed numerical simulations to study the response of magnetohydrodynamics (MHD) to large-scale stochastic forcing mechanisms parametrized by one parameter, $0 \le a \le1$, going from direct injection on the velocity field ($a = 1$) to stirring acts on the magnetic field only ($a = 0$). We study the multi-scale properties of the energy transfer, by splitting the total flux in channels mediated by (i) the kinetic non-linear advection, (ii) the Lorentz force, (iii) the magnetic advection and (iv) magnetic stretching term. We further decompose the fluxes in two sub-channels given by heterochiral and homochiral components in order to distinguish forward, inverse and flux-loop cascades. We show that there exists a quasi-singular role of the magnetic forcing mechanism for $a \sim 1$: a small injection on the magnetic field $a < 1$ can strongly deplete the mean flux of kinetic energy transfer throughout the kinetic non-linear advection channel. We also show that this negligible mean flux is the result of a flux-loop balance between heterochiral (direct) and homochiral (inverse) transfers. Conversely, both homochiral and heterochiral channels transfer energy forward for the other three channels. Cross exchange between velocity and the magnetic field is reversed around $a = 0.4$ and except when $a \sim 1$ we always observe that heterochiral mixed velocity-magnetic energy triads tend to move energy from magnetic to velocity fields. Our study is an attempt to further characterize the multi-scale nature of MHD dynamics, by disentangling different properties of the total energy transfer mechanisms, which can be useful for improving sub-grid-modelling.