Sustaining turbulence in spectrally stable shear flows – interplay of linear transient growth and nonlinear transverse cascade

¹ Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
² Helmholtz-Zentrum Dresden-Rossendorf, P.O. Box 510119, 01314 Dresden, Germany
³ Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712, USA
⁴ Abastumani Astrophysical Observatory, Ilia State University, Tbilisi 0162, Georgia

Abstract

We analyze the sustaining mechanism of nonlinear perturbations/turbulence in spectrally stable smooth shear flows. The essence of the sustenance is a subtle interplay of linear transient growth of Fourier harmonics and nonlinear processes. In spectrally stable shear flows, the transient growth of perturbations is strongly anisotropic in spectral (k-)space. This, in turn, leads to anisotropy of nonlinear processes in k-space and, as a result, the main (new) 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 nonlinear state is sustained owing to the interplay of the linear nonmodal growth and the transverse cascade. The possibility of such course of events has been described in k-space by G. Chagelishvili, J.-P. Zahn, A. Tevzadze and J. Lominadze, A&A, 402, 401 (2003) that reliably exemplifies the well-known bypass scenario of subcritical turbulence in spectrally stable shear flows. We present selected results of the simulations performed in different (HD and MHD; 2D and 3D; plane and Keplerian) shear flows to demonstrate the transverse cascade in action.