Forced MHD turbulence in three dimensions using Taylor-Green symmetries

TL;DR

This study investigates the scaling laws of three-dimensional MHD turbulence under Taylor-Green symmetries with various forcing functions, revealing different spectral behaviors and analyzing energy ratios and turbulence regimes through high-resolution simulations.

Contribution

It introduces a comprehensive numerical analysis of MHD turbulence with Taylor-Green symmetries, exploring different forcing scenarios and their impact on spectral laws and turbulence regimes.

Findings

Different spectral indices emerge, including Kolmogorov, Iroshnikov-Kraichnan, and weak turbulence.

The inertial range dynamics depend on the ratios of kinetic to magnetic energy.

Temporal variations of turbulence quasi-equilibria are analyzed.

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 $2048^3$ 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 Alfv\'en 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 Alfv\'en time, and analyze the temporal variations of these quasi-equilibria.