Scale Locality of Magnetohydrodynamic Turbulence

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Abstract
We investigate the scale locality of cascades of conserved invariants at high kinetic and magnetic Reynold's 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\char22{}or, equivalently, fluxes of Els\"asser energies\char22{}are dominated by the contributions of local triads. Flux of magnetic helicity may be dominated by nonlocal triads. The magnetic stretching term may also be dominated by nonlocal 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 10243 simulation of forced MHD turbulence.
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