On the Anisotropic Nature of MRI-driven Turbulence in Astrophysical Disks

The magnetorotational instability (MRI) is thought to play an important role in enabling accretion in sufficiently ionized astrophysical disks. The rate at which MRI-driven turbulence transports angular momentum is intimately related to both the strength of the amplitudes of the fluctuations on various scales and the degree of anisotropy of the underlying turbulence. This has motivated several studies to characterize the distribution of turbulent power in spectral space. In this paper we investigate the anisotropic nature of MRI-driven turbulence using a pseudo-spectral code and introduce novel ways for providing a robust characterization of the underlying turbulence. We study the growth of the MRI and the subsequent transition to turbulence via parasitic instabilities, identifying their potential signature in the late linear stage. We show that the general flow properties vary in a quasi-periodic way on timescales comparable to ∼10 inverse angular frequencies, motivating the temporal analysis of its anisotropy. We introduce a 3D tensor invariant analysis to quantify and classify the evolution of the anisotropy of the turbulent flow. This analysis shows a continuous high level of anisotropy, with brief sporadic transitions toward two- and three-component isotropic turbulent flow. This temporal-dependent anisotropy renders standard shell averaging especially when used simultaneously with long temporal averages, inadequate for characterizing MRI-driven turbulence. We propose an alternative way to extract spectral information from the turbulent magnetized flow, whose anisotropic character depends strongly on time. This consists of stacking 1D Fourier spectra along three orthogonal directions that exhibit maximum anisotropy in Fourier space. The resulting averaged spectra show that the power along each of the three independent directions differs by several orders of magnitude over most scales, except the largest ones. Our results suggest that a first-principles theory to describe fully developed MRI-driven turbulence will likely have to consider the anisotropic nature of the flow at a fundamental level.