Mechanism and structure of turbulence predicted by statistical state dynamics is verified in Couette flow by DNS

Brian F. Farrell, Petros J. Ioannou, Marios-Andreas Nikolaidis

Published 2018-08-11Version 1

The no-slip boundary condition results in a velocity shear forming in fluid flow near a solid surface. This shear flow supports the turbulence characteristic of fluid flow near boundaries at Reynolds numbers above $\approx 1000$ by making available to perturbations the kinetic energy of the externally forced flow. Understanding the physical mechanism underlying transfer of energy from the forced mean flow to the turbulent perturbation field that is required to maintain turbulence poses a fundamental question. Although qualitative understanding that this transfer involves nonlinear destabilization of the roll-streak coherent structure has been established, identification of this instability has resisted analysis. The reason this instability has resisted comprehensive analysis is that its analytic expression lies in the Navier-Stokes equations (NS) expressed using statistical rather than state variables. Expressing NS as a statistical state dynamics (SSD) at second order in a cumulant expansion suffices to allow analytical identification of the nonlinear instability underlying turbulence in wall-bounded shear flow. In this nonlinear instability the turbulent perturbation field is identified by the SSD with the Lyapunov vectors of the linear operator governing perturbation evolution about the time dependent streamwise mean flow. In this work predictions of SSD analysis that this parametric instability underlies the dynamics of turbulence in Couette flow and that the perturbation structures are the associated Lyapunov vectors and that suppressing only the top few of these vectors results in laminarization are verified using DNS.