Strong anisotropy in quasi-static magnetohydrodynamic turbulence for high interaction parameters

We simulate forced quasi-static magnetohydrodynamic turbulence and investigate the anisotropy, energy spectrum, and energy flux of the flow, specially for large interaction parameters ($N$). We show that the angular dependence of the energy spectrum is well quantified using Legendre polynomials. For large $N$, the energy spectrum is exponential. Our direct computation of energy flux reveals an inverse cascade of energy at low wavenumbers, similar to that in two-dimensional turbulence. We observe the flow be two-dimensional (2D) for moderate $N$ ($N \sim 20$), and two-dimensional three-component (2D-3C) type for $N \ge 27$. In our forced simulation, the transition from 2D to 2D-3C occurs at higher value of $N$ than Favier et al., ["On the two-dimensionalization of quasistatic magnetohydrodynamic turbulence," Phys. Fluids 22, 075104 (2010)] who employ decaying simulations.