Dual cascade of kinetic and magnetic energy in MHD turbulence

Using scale-locality of the energy cascade in MHD turbulence, which we have rigorously shown to hold in [1], we prove that the kinetic and magnetic energy budgets statistically decouple beyond a ``conversion'' range. Over the ensuing part of the inertial range, mean kinetic and magnetic energies cascade to smaller scales independently. In other words, we show that magnetic-line stretching acts as a \emph{large-scale} forcing of the magnetic field which vanishes, on average, deep in the inertial range. We present numerical support from $1024^3$ direct numerical simulations. We draw analogies to such a phenomenon from compressible turbulence and geophysical flows and discuss its possible implications on MHD turbulence simulations.\\[4pt] [1] Aluie, H., Eyink, G. L., Phys. Rev. Lett., 104, 8, 081101 (2010)