The dynamics of unforced turbulence at high Reynolds number for Taylor-Green vortices generalized to MHD

TL;DR

This study investigates high Reynolds number MHD turbulence from Taylor-Green vortices, revealing accelerated decay, quasi-constant dissipation intervals, and weak turbulence spectra, using advanced pseudo-spectral simulations with symmetry optimizations.

Contribution

It extends the Taylor-Green vortex analysis to MHD at high Reynolds numbers, demonstrating accelerated turbulence evolution and detailed small-scale structure development.

Findings

Accelerated turbulence decay in MHD compared to neutral fluids.

Identification of a quasi-constant dissipation interval.

Observation of weak turbulence spectra and complex current structures.

Abstract

We study decaying magnetohydrodynamics (MHD) turbulence stemming from the evolution of the Taylor-Green (TG) flow generalized recently to MHD, with equal viscosity and magnetic resistivity and up to equivalent grid resolutions of 2048^3 points. A pseudo-spectral code is used in which the symmetries of the velocity and magnetic fields have been implemented, allowing for sizable savings in both computer time and usage of memory at a given Reynolds number. The flow is non-helical, and at initial time the kinetic and magnetic energies are taken to be equal and concentrated in the large scales. After testing the validity of the method on grids of 512^3 points, we analyze the data on the large grids up to Taylor Reynolds numbers of ~2200. We find that the global temporal evolution is accelerated in MHD, compared to the corresponding neutral fluid case. We also observe an interval of time when such configurations have quasi-constant total dissipation, time during which statistical properties are determined after averaging over of the order of two turn-over times. A weak turbulence spectrum obtains which is also given in terms of its anisotropic components. Finally, we contrast the development of small-scale eddies with two other initial conditions for the magnetic field and briefly discuss the structures that develop, and which display a complex array of current and vorticity sheets with clear rolling-up and folding.