Forced MHD turbulence in three dimensions using Taylor-Green symmetries
arXiv:1212.6902
Abstract
We examine the scaling laws of MHD turbulence for three different types of forcing functions and imposing at all times the four-fold symmetries of the Taylor-Green (TG) vortex generalized to MHD; no uniform magnetic field is present and the magnetic Prandtl number is equal to unity. We also include a forcing in the induction equation, and we take the three configurations studied in the decaying case in [E. Lee et al. Phys. Rev.E {\bf 81}, 016318 (2010)]. To that effect, we employ direct numerical simulations up to an equivalent resolution of grid points. We find that, similarly to the case when the forcing is absent, different spectral indices for the total energy spectrum emerge, corresponding to either a Kolmogorov law, an Iroshnikov-Kraichnan law that arises from the interactions of turbulent eddies and Alfvén waves, or to weak turbulence when the large-scale magnetic field is strong. We also examine the inertial range dynamics in terms of the ratios of kinetic to magnetic energy, and of the turn-over time to the Alfvén time, and analyze the temporal variations of these quasi-equilibria.