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

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.

16 pages, 10 figures. Submitted to GAFD

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• Structures and dynamics of small scales in decaying magnetohydrodynamic turbulence
• Ideal evolution of MHD turbulence when imposing Taylor-Green symmetries
• A new class of finite element variational multiscale turbulence models for incompressible magnetohydrodynamics
• Turbulent cascade, bottleneck and thermalized spectrum in hyperviscous flows
• Long-time properties of MHD turbulence and the role of symmetries
• Scale dependence and cross-scale transfer of kinetic energy in compressible hydrodynamic turbulence at moderate Reynolds numbers
• The effect of helicity on the correlation time of large scale turbulent flows
• The origins of $k^{-2}$ spectrum in the decaying Taylor-Green magnetohydrodynamic turbulent flows
• Self-truncation and scaling in Euler-Voigt-$\alpha$ and related fluid models
• Magnetized Decaying Turbulence in the Weakly Compressible Taylor-Green Vortex