Nonlinear transverse cascade—A key factor of sustenance of subcritical turbulence in shear flows

Abstract

We analyze the essence of nonlinear processes that underlie turbulence sustenance in spectrally stable shear flows. In these flows, the strong anisotropy of velocity shear-induced nonmodal growth phenomenon in spectral (k-)space, in turn, entails the anisotropy of nonlinear processes in this space. Consequently, the main novel nonlinear process is transverse, or angular redistribution of modes in Fourier space referred to as the nonlinear transverse cascade rather than a mere direct/inverse cascade. It is demonstrated that nonlinear coherent as well as turbulent states are sustained via a subtle interplay of the linear nonmodal growth (that has transient nature) and the nonlinear transverse cascade. This course of events exemplifies the well-known bypass scenario of subcritical turbulence in spectrally stable shear flows. In this proceedings paper, we present selected results of our simulations of hydrodynamic and MHD 2D plane shear flows to demonstrate the transverse cascade in action.