The essence of onset and self-sustenance of turbulence in astrophysical shear flows Sources

Abstract

To understand the mechanism of the self-sustenance of subcritical turbulence in spectrally stable astrophysical (constant) shear flows, we performed direct numerical simulations of turbulence in plane hydrodynamic and MHD homogeneous shear flows in the local shearing-box approximation with subsequent analysis of the dynamical processes in spectral/Fourier space. In the MHD case, we considered uniform magnetic field directed parallel to the flow. There are no exponentially growing modes in such flows and the turbulence is instead energetically supported only by the linear transient growth of Fourier harmonics of perturbations due to the shear flow non-normality. This non-normality-induced growth, also known as nonmodal growth, is anisotropic in Fourier space, which, in turn, leads to a specific anisotropy of nonlinear processes in this space. As a result, a main nonlinear process in shear flows is transverse (angular) redistribution of harmonics in Fourier space – nonlinear transverse cascade – rather than usual direct or inverse cascades. It is demonstrated that the turbulence is sustained by a subtle interplay between the linear nonmodal growth and the nonlinear transverse cascade for all considered flow configurations. The only energy supplier for the turbulence is the linear transient growth of perturbations due to the flow shear, which is mediated by Reynolds and Maxwell stresses, extracting, respectively, kinetic and magnetic energy from the background flow – the nonlinear processes do not directly change the total perturbation energy but only redistribute it among Fourier harmonics of perturbations. We propose the basic cycles of the turbulence sustenance in the considered cases, which clearly show the synergy of linear and nonlinear processes in the self-organization of the flow. Performing numerical simulations for different values of the background magnetic field, we show that with the increase of the field, the onset of turbulence occurs at larger times and the power of turbulence reduces. Finally, at definite threshold background magnetic field the flow completely stabilizes. It is significant that, there is an essential difference in the energy supply of plane and rotating/Keplerian astrophysical shear flows: in plane shear flows the leading linear process energetically supplying turbulence is due to the kinematics (Reynolds stress), while for Keplerian rotation – is due to magnetic field (Maxwell stress).