Numerical simulations of driven relativistic magnetohydrodynamic turbulence

A wide variety of astrophysical phenomena involve the flow of turbulent magnetized gas with relativistic velocity or energy density. Examples include gamma-ray bursts, active galactic nuclei, pulsars, magnetars, micro-quasars, merging neutron stars, X-ray binaries, some supernovae, and the early universe. In order to elucidate the basic properties of the relativistic magnetohydrodynamical (RMHD) turbulence present in these systems, we present results from numerical simulations of fully developed driven turbulence in a relativistically warm, weakly magnetized and mildly compressible ideal fluid. We have evolved the RMHD equations for many dynamical times on a uniform grid with 1024³ zones using a high-order Godunov code. We observe the growth of magnetic energy from a seed field through saturation at ∼1% of the total fluid energy. We compute the power spectrum of velocity and density-weighted velocity U = ρ^1/3 v and conclude that the inertial scaling is consistent with a slope of -5/3. We compute the longitudinal and transverse velocity structure functions of order p up to 11 and discuss their possible deviation from the expected scaling for non-relativistic media. We also compute the scale-dependent distortion of coherent velocity structures with respect to the local magnetic field, finding a weaker scale dependence than is expected for incompressible non-relativistic flows with a strong mean field.