MHD turbulence in Keplerian disks with net azimuthal magnetic field - bypass concept of self-sustenance via interplay of linear transient growth and nonlinear transverse cascade

We studied the mechanism of the self-sustenance of MHD turbulence in spectrally stable stratified Keplerian disk flows threaded by nonzero net azimuthal magnetic field in the shearing box approximation. For this purpose, we performed direct numerical simulations of (homogeneous, subcritical) turbulence at different aspect ratios of the simulation boxes. Then, we analyzed the turbulence dynamics in Fourier/wavenumber/spectral space based on the simulation data to gain deeper insight into the self-sustaining dynamics of such subcritical MHD turbulence. Specifically, we examined the interplay of linear transient growth of Fourier harmonics and nonlinear processes. In the case of azimuthal field in the shearing box setup, the linear growth of (magnetic) perturbations has a transient nature and is strongly anisotropic in spectral space. This, in turn, leads to anisotropy of nonlinear processes in spectral space and, as a result, the main nonlinear process appears to be not a direct/inverse, but rather a transverse/angular redistribution of harmonics in Fourier space referred to as the nonlinear transverse cascade. It is demonstrated that the turbulence is sustained by interplay of the linear transient growth and the transverse cascade. The main scheme of this interplay in Keplerian disks was first proposed in Chagelishvili, Zahn, et al. (2003) and then its realization in real flows has been investigated in our recent papers Horton et al. (2010), Mamatsashvili et al. (2014, 2016). This scheme exemplifies the bypass concept of subcritical turbulence in spectrally stable shear flows. Both transient growth and transverse cascade mainly operate at large length scales, comparable to the box size. Consequently, the central, small wavenumber area of Fourier space is crucial in the self-sustenance of the turbulence and is labeled as the vital area. Outside the vital area both transient growth and transverse cascade are of secondary importance - Fourier harmonics are transferred to dissipative scales by the usual nonlinear direct cascade.