Analysis of energy transfer through direct numerical simulations of magnetohydrodynamic Orszag–Tang vortex

Abstract

Direct numerical simulations of magnetohydrodynamic turbulence with Orszag–Tang vortex initial conditions are presented here for two different Reynolds numbers. Simulations of this transition-to-turbulence problem are carried out using a pseudo-spectral code with a grid resolution fine enough to resolve the Kolmogorov scale. The power-law behavior of bulk quantities like kinetic energy, magnetic energy, integral length scales, and enstrophy is analyzed. For a low Reynolds number, weak turbulence spectra are observed with a slope of −2.0 in the inertial subrange, while for a higher Reynolds number, the spectra exhibit a slope very close to the Kolmogorov spectra of −5/3. The Q-criteria isosurfaces at the time instant of maximum enstrophy are used for the visualization of turbulence developed within the flow. Furthermore, a new approach is presented to understand the dynamics of the transfer between kinetic and magnetic energies in the early period of development using the energy flux spectra, rate of change of kinetic and magnetic energies, and current density structures, which employ a three-dimensional representation of the alignment between velocity and magnetic field across the structures.