As a matter of dynamical range -- scale dependent energy dynamics in MHD turbulence

TL;DR

This study investigates the energy transfer mechanisms in MHD turbulence through high-resolution simulations, revealing that energy fluxes are scale-dependent and questioning the existence of a universal asymptotic regime.

Contribution

It introduces a framework to analyze energy transfer in MHD turbulence and demonstrates the non-constancy of energy fluxes across scales, challenging previous assumptions.

Findings

All ILES calculations are resolved and equivalent to visco-resistive MHD.

Increasing grid resolution lowers dissipation coefficients, raising Reynolds numbers.

No convergence observed at high resolution, questioning the existence of an asymptotic regime.

Abstract

Magnetized turbulence is ubiquitous in many astrophysical and terrestrial plasmas but no universal theory exists. Even the detailed energy dynamics in magnetohydrodynamic (MHD) turbulence are still not well understood. We present a suite of subsonic, super-Alfv\'enic, high plasma-beta MHD turbulence simulations that only vary in their dynamical range, i.e., in their separation between the large-scale forcing and dissipation scales, and their dissipation mechanism (implicit large eddy simulation, ILES, versus and direct numerical simulation, DNS). Using an energy transfer analysis framework we calculate the effective, numerical viscosities and resistivities and demonstrate and that all ILES calculations of MHD turbulence are resolved and correspond to an equivalent visco-resistive MHD turbulence calculation. Increasing the number of grid points used in an ILES corresponds to lowering the dissipation coefficients, i.e., larger (kinetic and magnetic) Reynolds numbers for a constant forcing scale. Independently, we use this same framework to demonstrate that -- contrary to hydrodynamic turbulence -- the cross-scale energy fluxes are not constant in MHD turbulence. This applies both to different mediators (such as cascade processes or magnetic tension) for a given dynamical range as well as to a dependence on the dynamical range itself, which determines the physical properties of the flow. We do not observe any indication of convergence even at the highest resolution (largest Reynolds numbers) simulation at $2{,}048^3$ cells, calling into question whether an asymptotic regime in MHD turbulence exists, and, if so, what it looks like.