Analytic characterization of sub-Alfv\'enic turbulence energetics

TL;DR

This paper analytically characterizes the energy exchange in sub-Alfvénic MHD turbulence, revealing how magnetic energy transfers to kinetic energy through coupling mechanisms, supported by numerical validation.

Contribution

It provides an analytical framework for understanding the energetics of compressible, sub-Alfvénic turbulence, resolving previous puzzles about energy imbalance.

Findings

Magnetic energy transfer is primarily through coupling between ordered and fluctuating magnetic fields.

Analytical relations match numerical data up to second order terms.

Kinetic energy can vastly exceed magnetic energy in strongly magnetized turbulence.

Abstract

Magnetohydrodynamic (MHD) turbulence is a cross-field process relevant to many systems. A prerequisite for understanding these systems is to constrain the role of MHD turbulence, and in particular the energy exchange between kinetic and magnetic forms. The energetics of strongly magnetized and compressible turbulence has so far resisted attempts to understand them. Numerical simulations reveal that kinetic energy can be orders of magnitude larger than fluctuating magnetic energy. We solve this lack-of-balance puzzle by calculating the energetics of compressible and sub-Alfv\'enic turbulence based on the dynamics of coherent cylindrical fluid parcels. Using the MHD Lagrangian, we prove analytically that the bulk of the magnetic energy transferred to kinetic is the energy stored in the coupling between the ordered and fluctuating magnetic field. The analytical relations are in striking agreement with numerical data, up to second order terms.