Large eddy simulations of high-magnetic Reynolds number magnetohydrodynamic turbulence for non-helical and helical initial conditions: A study of two sub-grid scale models

Abstract

Pseudo-spectral large eddy simulation (LES) calculations of high-magnetic Reynolds number (Rem) incompressible magnetohydrodynamic (MHD) turbulence are carried out for two initial conditions, namely, the non-helical Orszag–Tang vortex and the strongly helical Arnold–Beltrami–Childress (ABC) flows using two eddy-viscosity-based sub-grid scale (SGS) approaches: the cross-helicity (CH) and dynamic Smagorinsky (DS) models. Validation is conducted through comparisons of 1923 LES calculations with in-house 5123 direct numerical simulations (DNS) at Reynolds number, Re=Rem=800. The results show that the CH model performs better than the DS model. The performance of the SGS models at higher Re is further evaluated by carrying out 3843 LES calculations at Re=Rem=7500. Various quantities including turbulent kinetic energy, turbulent magnetic energy, cross-helicity, helicity, vorticity structures, cosine of angle between velocity and magnetic field, cosine of angle between velocity and vorticity field, kinetic and magnetic energy spectra, and energy fluxes are analyzed to understand the capability of the two LES models in predicting the evolution of MHD turbulence. The higher Reynolds number flow shows a delay in the maximum dissipation with increased transfer of energy toward small scales, resulting in a −5/3 Kolmogorov inertial sub-range scaling. In addition, the effect of Reynolds number on the alignment between velocity and magnetic field, and the energy transfer between kinetic and magnetic energy, is studied. With the ABC flow having strong helicity and zero cross-helicity at low and high Reynolds numbers, a strong dynamo effect is also observed using the LES models, which is consistent with previous DNS.