Energy partition in magnetohydrodynamic turbulence

TL;DR

This paper derives a simple method to analyze energy distribution in MHD turbulence, revealing conditions for equipartition between kinetic and magnetic energies based on turbulent lengthscales.

Contribution

It introduces a straightforward approach to determine energy partition in MHD turbulence, building on previous foundational studies by Lee and Chandrasekhar.

Findings

Turbulent viscous and ohmic dissipations are comparable.

Energy ratio depends on the ratio of magnetic to velocity lengthscales.

Equipartition occurs when the largest eddy lengthscales are similar.

Abstract

We use a simple and straightforward method to derive the energy partition in magnetohydrodynamics (MHD) turbulence that was first studied by Lee and then more rigorously by Chandrasekhar. By investigating the energy equation we find that the turbulent viscous and ohmic dissipations are comparable to each other. Under the condition that turbulent viscosity and turbulent magnetic diffusivity are comparable, we deduce that the ratio of kinetic to magnetic energies depends on the ratio of the turbulent magnetic lengthscale to turbulent velocity lengthscale of the largest eddies. When the two largest lengthscales are comparable, the two energies are in equipartition.