MHD turbulence in shear flows and Keplerian disks - sustenance via interplay of linear nonmodal growth and nonlinear transverse cascade


MHD turbulence in shear flows and Keplerian disks - sustenance via interplay of linear nonmodal growth and nonlinear transverse cascade

Mamatsashvili, G.

We investigate MHD turbulence in spectrally stable shear flows, including Keplerian disk flows, threaded by a non-zero net azimuthal/toroidal magnetic field. In order to gain a deeper insight into its sustaining mechanism, we performed a set of numerical simulations in the shearing box model and based on the simulation data, analyzed in detail the turbulence dynamics in Fourier/wavenumber k-space. Classical exponential/modal instabilities are absent in such flows and linear growth of perturbations has a transient nature due to shear flow non-normality, also referred to as nonmodal growth. Similarly, in the case of Keplerian flow with a net azimuthal field in the shearing box setup, the combination of rotation, shear and magnetic field, gives rise to the magnetorotational instability (MRI), which is dominated by the effects of non-normality and hence is of transient type too. This transient growth, which serves as the only energy supply to turbulence, is strongly anisotropic in Fourier space that, in turn, leads to anisotropy of nonlinear processes in Fourier space and, as a result, the main nonlinear process appears to be not an usual direct/inverse, but rather a new type of transverse/angular redistribution of perturbation modes in Fourier space, which we refer to as the nonlinear transverse cascade. We demonstrate that the turbulence is sustained by a subtle interplay of the linear nonmodal growth (transient MRI in the case of Keplerian disks) and the nonlinear transverse cascade. Analyzing this interplay, we reveal the basic subcycle of the sustenance scheme that clearly shows synergy of the linear and nonlinear processes in the self-organization of the magnetized flow system. This synergy is quite robust and persists for the considered four simulation boxes with different aspect ratios. The spectral characteristics of the dynamical processes in these boxes are qualitatively similar, indicating the universal character of the interplay that ensures the sustenance of the turbulence. Such an interplay of linear and nonlinear processes in the turbulence sustenance proposed here exemplifies the bypass concept of subcritical turbulence in spectrally stable shear flows, elaborated in the 1990s by the hydrodynamical community. Both the linear nonmodal growth and nonlinear 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 turbulence sustenance process and is called the vital area. Outside the vital area, both these processes are of secondary importance – the harmonics are transferred to dissipative scales by the usual nonlinear direct cascade only. In the conclusion, we discuss the application of this approach and results to the MRI-turbulence in Keplerian flows with vertical net nonzero or zero magnetic flux.

Keywords: MHD; nonmodal growth; magnetorotational instability; turbulence; accretion disks; numerical simulations

  • Invited lecture (Conferences)
    Invited seminar at the Niels Bohr Institute, University of Copenhagen, 24.-28.04.2017, Copenhagen, Denmark

Permalink: https://www.hzdr.de/publications/Publ-25859
Publ.-Id: 25859