Nonlinear Transverse Cascade and Sustenance of MRI Turbulence in Keplerian Disks with an Azimuthal Magnetic Field

We investigate magnetohydrodynamic turbulence driven by the magnetorotational instability (MRI) in Keplerian disks with a nonzero net azimuthal magnetic field using shearing box simulations. As distinct from previous studies, we analyze turbulence dynamics in Fourier (k-) space to understand its sustenance. The linear growth of the MRI with the azimuthal field has a transient character and is anisotropic in Fourier space, leading to anisotropy of nonlinear processes in Fourier space. As a result, the main nonlinear process appears to be a new type of angular redistribution of modes in Fourier space—the nonlinear transverse cascade—rather than the usual direct/inverse cascade. We demonstrate that the turbulence is sustained by the interplay of the linear transient growth of the MRI (which is the only energy supply for the turbulence) and the transverse cascade. These two processes operate at large length scales, comparable to the box size (disk scale height); the corresponding small wavenumber area, called the vital area in Fourier space, is crucial for the sustenance, while outside the vital area, direct cascade dominates. The interplay of the linear and nonlinear processes in Fourier space is generally too intertwined for a vivid schematization. Nevertheless, we reveal the basic subcycle of the sustenance that clearly shows the synergy of these processes in the self-organization of the magnetized flow system. This synergy is quite robust and persists for the considered different aspect ratios of the simulation boxes. The spectral characteristics of the dynamical processes in these boxes are qualitatively similar, indicating the universality of the sustenance mechanism of the MRI turbulence.