On the turbulence spectrum for compressive modes in astrophysical applications

Accretion flows onto supermassive black holes are magnetized and vigorously turbulent. Magnetically arrested disks are the leading scenarios for accretion onto black holes in our galaxy, Sgr A* and M87. Despite its significance, the properties of turbulence in these flows remain largely unexplored. In this paper we present initial analysis of turbulence spectra in an extremely high-resolution H-AMR simulation data (effective resolution of 5376 $\times$ 2304 $\times$ 230 cells) used to solve the general relativistic magnetohydrodynamics (GRMHD) equations for a spinning black hole in Kerr–Schild coordinates. We identify an inertial interval with a spectral index $-3/2$ in the turbulent disk for the plasma kinetic energy in the accretion disk near the event horizon.