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We investigate magnetohydrodynamic turbulence driven by the magnetorotationalinstability (MRI) in Keplerian disks with a nonzero net azimuthal magneticfield using shearing box simulations. As distinct from most previous studies,we analyze turbulence dynamics in Fourier (${\bf k}$-) space to understand itssustenance. The linear growth of MRI with azimuthal field has a transientcharacter and is anisotropic in Fourier space, leading to anisotropy ofnonlinear processes in Fourier space. As a result, the main nonlinear processappears to be a new type of angular redistribution of modes in Fourier space --the \emph{nonlinear transverse cascade} -- rather than usual direct/inversecascade. We demonstrate that the turbulence is sustained by interplay of thelinear transient growth of MRI (which is the only energy supply for theturbulence) and the transverse cascade. These two processes operate at largelength scales, comparable to box size and the corresponding small wavenumberarea, called \emph{vital area} in Fourier space is crucial for the sustenance,while outside the vital area direct cascade dominates. The interplay of thelinear and nonlinear processes in Fourier space is generally too intertwinedfor a vivid schematization. Nevertheless, we reveal the \emph{basic subcycle}of the sustenance that clearly shows synergy of these processes in theself-organization of the magnetized flow system. This synergy is quite robustand persists for the considered different aspect ratios of the simulationboxes. The spectral characteristics of the dynamical processes in these boxesare qualitatively similar, indicating the universality of the sustenancemechanism of the MRI-turbulence.

Nonlinear transverse cascade and sustenance of MRI-turbulence in Keplerian disks with an azimuthal magnetic field