Decoupling of the Kinetic and Magnetic Energy Cascades in MHD Turbulence

Abstract

Magnetic and kinetic energy in ideal incompressible MHD are not global invariants and, therefore, it had been justified to discuss only the cascade of their sum, total energy. We provide a physical argument based on scale-locality of the cascade, along with compelling evidence that at high Reynolds numbers, magnetic and kinetic energy budgets statistically decouple beyond a transitional "conversion" range. This arises because magnetic field-line stretching is a large-scale process which vanishes on average at intermediate and small scales within the inertial-inductive range, thereby allowing each of mean kinetic and magnetic energy to cascade conservatively and at an equal rate. One consequence is that the turbulent magnetic Prandtl number is unity over the "decoupled range" of scales.