Inertial range of magnetorotational turbulence

Accretion of matter onto a compact object is triggered by turbulence driven by magnetorotational instability (MRI). While there have been numerous theoretical and computational studies on MRI turbulence in the past few decades, the inertial range of MRI turbulence remains poorly understood. For instance, both the magnetic and kinetic energy spectra deviate significantly from those predicted by theories of MHD turbulence and those observed in simulations of externally driven MHD turbulence. This discrepancy arises due to the fact that the energy injection via MRI happens broadly in a Fourier space, posing challenges for numerically resolving the inertial range. In this colloquium, I will present the numerically resolved inertial range of MRI turbulence using Rotational Reduced MHD (RRMHD) model. This model assumes the presence of a near-azimuthal mean magnetic field and considers small amplitude turbulent fluctuations elongated along the mean magnetic field. By making these assumptions, RRMHD allows us to reach the inertial range with minimal computational resources. Our findings include: (1) both magnetic and kinetic energy exhibit -3/2 spectra, (2) Alfvenic fluctuations and slow-mode-like compressive fluctuations are decoupled at small scales, and (3) compressive fluctuations are approximately twice as strong as Alfvenic fluctuations. Furthermore, we will show our ultra-high resolution simulation of MRI turbulence using standard MHD and demonstrate that the small-scale spectra closely resemble those of RRMHD, thereby validating the RRMHD approach.