Scale-Locality of Magnetohydrodynamic Turbulence

TL;DR

This paper proves that in high Reynolds number MHD turbulence, energy and cross-helicity fluxes are primarily local, while magnetic helicity transfer can be non-local, supported by high-resolution simulation data.

Contribution

It provides a rigorous proof of the scale-locality of energy and cross-helicity fluxes in MHD turbulence and clarifies the conditions under which magnetic helicity transfer can be non-local.

Findings

Energy and cross-helicity fluxes are dominated by local triads.

Magnetic helicity transfer may be dominated by non-local triads.

Simulation data supports the theoretical findings.

Abstract

We investigate the scale-locality of cascades of conserved invariants at high kinetic and magnetic Reynolds numbers in the ``inertial-inductive range'' of magnetohydrodynamic (MHD) turbulence, where velocity and magnetic field increments exhibit suitable power-law scaling. We prove that fluxes of total energy and cross-helicity--or, equivalently, fluxes of Els\"asser energies--are dominated by the contributions of local triads. Corresponding spectral transfers are also scale-local when defined using octave wavenumber bands. Flux and transfer of magnetic helicity may be dominated by non-local triads. The magnetic stretching term also may be dominated by non-local triads but we prove that it can convert energy only between velocity and magnetic modes at comparable scales. We explain the disagreement with numerical studies that have claimed conversion nonlocally between disparate scales. We present supporting data from a $1024^3$ simulation of forced MHD turbulence.