Alfvén-dynamo balance and magnetic excess in magnetohydrodynamic turbulence

¹ LPP, École Polytechnique, Route de Saclay, 91120 Palaiseau, France
e-mail: Roland.Grappin@lpp.polytechnique.fr
² Technische Universität Berlin, Zentrum für Astronomie und Astrophysik, Hardenbergstr. 36A, 10623 Berlin, Germany
³ Università di Firenze, Dipartimento di Fisica e Astronomia Largo Fermi, 50125 Firenze, Italy and Royal Observatory of Belgium, SIDC/STCE, 3 avenue circulaire, 1180 Brussels, Belgium

Received: 8 January 2016
Accepted: 9 March 2016

Abstract

Context. Three-dimensional magnetohydrodynamic (3D MHD) turbulent flows with initially magnetic and kinetic energies at equipartition spontaneously develop a magnetic excess (or residual energy) in both numerical simulations and the solar wind. Closure equations obtained in 1983 describe the residual spectrum as resulting from a balance between a dynamo source proportional to the total energy spectrum and a linear Alfvén damping term. A good agreement was found in 2005 with incompressible simulations; however, recent solar wind measurements disagree with these results.

Aims. The previous dynamo-Alfvén theory is generalized to a family of models, leading to simple relations between residual and total energy spectra. We want to assess these models in detail against MHD simulations and solar wind data.

Methods. We tested the family of models against compressible decaying MHD simulations with a low Mach number, low cross-helicity, and zero-mean magnetic field with or without expansion terms (EBM; expanding box model).

Results. A single dynamo-Alfvén model is found to describe correctly both solar wind scalings and compressible simulations without or with expansion. This model is equivalent to the 1983–2005 closure equation, but it incorporates the critical balance of nonlinear turnover and linear Alfvén times, while the dynamo source term remains unchanged. We elucidate the discrepancy with previous incompressible simulations. The model predicts a linear relation between the spectral slopes of total and residual energies m_R = −1/2 + 3/2m_T. By examining previous solar wind data, our relation is found to be valid for any cross-helicity, and is even better at high cross-helicity with the total energy slope varying from 1.7 to 1.55.