Active Modes and Dynamical Balances in MRI Turbulence of Keplerian Disks with a Net Vertical Magnetic Field

We studied dynamical balances in magnetorotational instability (MRI) turbulence with a net vertical field in the shearing box model of disks. Analyzing the turbulence dynamics in Fourier (k-) space, we identified three types of active modes that define the turbulence characteristics. These modes have lengths similar to the box size, i.e., lie in the small wavenumber region in Fourier space labeled "the vital area" and are (i) the channel mode, uniform in the disk plane with the smallest vertical wavenumber; (ii) the zonal flow mode, azimuthally and vertically uniform with the smallest radial wavenumber; and (iii) the rest (parasitic) modes. The rest modes comprise those harmonics in the vital area whose energies reach more than 50% of the maximum spectral energy. The rest modes individually are not so significant compared to the channel and zonal flow modes; however, the combined action of their multitude is dominant over these two modes. These three mode types are governed by the interplay of the linear and nonlinear processes, leading to their interdependent dynamics. The linear processes consist of disk flow nonmodality modified classical MRI with a net vertical field. The main nonlinear process is the transfer of modes over wavevector angles in Fourier space-the transverse cascade. The channel mode exhibits episodic bursts supplied by linear MRI growth, while the nonlinear processes mostly oppose this, draining the channel energy and redistributing it to the rest modes. As for the zonal flow, it does not have a linear source and is fed by nonlinear interactions of the rest modes.