High Reynolds number magnetohydrodynamic turbulence using a Lagrangian model

TL;DR

This study uses a Lagrangian model to simulate high Reynolds number magnetohydrodynamic turbulence, revealing magnetic dominance, isotropic energy spectra, and deviations from critical balance at small scales.

Contribution

It extends previous MHD turbulence modeling to higher Reynolds numbers without forcing or uniform magnetic fields, providing new insights into spectral laws and anisotropy.

Findings

Magnetic field dominates the flow at high Reynolds numbers.

Energy spectrum follows Iroshnikov-Kraichnan law, with local Kolmogorov behavior perpendicular to the mean field.

The ratio of eddy turnover time to Alfvén time increases with wavenumber, challenging critical balance.

Abstract

With the help of a model of magnetohydrodynamic (MHD) turbulence tested previously, we explore high Reynolds number regimes up to equivalent resolutions of 6000^3 grid points in the absence of forcing and with no imposed uniform magnetic field. For the given initial condition chosen here, with equal kinetic and magnetic energy, the flow ends up being dominated by the magnetic field, and the dynamics leads to an isotropic Iroshnikov-Kraichnan energy spectrum. However, the locally anisotropic magnetic field fluctuations perpendicular to the local mean field follow a Kolmogorov law. We find that the ratio of the eddy turnover time to the Alfven time increases with wavenumber, contrary to the so-called critical balance hypothesis. Residual energy and helicity spectra are also considered; the role played by the conservation of magnetic helicity is studied, and scaling laws are found for the magnetic helicity and residual helicity spectra. We put these results in the context of the dynamics of a globally isotropic MHD flow which is locally anisotropic because of the influence of the strong large-scale magnetic field, leading to a partial equilibration between kinetic and magnetic modes for the energy and the helicity.