Analytic characterization of sub-Alfvénic turbulence energetics

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 higher than fluctuating magnetic energy. We solved this lack-of-balance puzzle by calculating the energetics of compressible and sub-Alfvénic turbulence based on the dynamics of coherent cylindrical fluid parcels. Using the MHD Lagrangian, we proved analytically that the bulk of the magnetic energy transferred to kinetic energy is the energy that is stored in the coupling between the ordered and fluctuating magnetic field. The analytical relations are in strikingly good agreement with numerical data, up to second-order terms.