# Decoupling of the Kinetic and Magnetic Energy Cascades in MHD Turbulence

## TL;DR

This paper demonstrates that in high Reynolds number MHD turbulence, magnetic and kinetic energy cascades become statistically independent beyond a certain scale, with each conserving energy separately and the magnetic Prandtl number approaching unity.

## Contribution

It provides a physical argument and evidence showing the decoupling of magnetic and kinetic energy cascades in MHD turbulence at high Reynolds numbers.

## Key findings

- Magnetic and kinetic energy budgets decouple beyond a transitional range.
- Magnetic field-line stretching vanishes at small scales.
- Magnetic Prandtl number approaches unity in the decoupled range.

## 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.