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The no-slip boundary condition results in a velocity shear forming in fluidflow near a solid surface. This shear flow supports the turbulencecharacteristic of fluid flow near boundaries at Reynolds numbers above$\approx1000$ by making available to perturbations the kinetic energy of theexternally forced flow. Understanding the physical mechanism underlying thisenergy transfer poses a fundamental question. Although qualitativeunderstanding that this transfer involves nonlinear destabilization of theroll-streak coherent structure has been established, identification of thisinstability has resisted analysis. The reason this instability has resistedanalysis is that its analytic expression lies in the Navier-Stokes equations(NS) expressed using statistical rather than state variables. Expressing NS asa statistical state dynamics (SSD) at second order in a cumulant expansionsuffices to allow analytical identification of the nonlinear roll-streakinstability underlying turbulence in wall-bounded shear flow. In this nonlinearinstability the turbulent perturbation field is identified by the SSD with theLyapunov vectors of the linear operator governing perturbation evolution aboutthe time-dependent streamwise mean flow. In this work, the implications of thepredictions of SSD analysis (that this parametric instability underlies thedynamics of turbulence in Couette flow and that the perturbation structures arethe associated Lyapunov vectors) are interpreted to imply new conceptualapproaches to controlling turbulence. It is shown that the perturbationcomponent of turbulence is supported on the streamwise mean flow, which impliesoptimal control should be formulated to suppress perturbations from thestreamwise mean. It is also shown that suppressing only the top few Lyapunovvectors on the streamwise mean vectors results in laminarization. These resultsare verified using DNS.

Parametric mechanism maintaining Couette flow turbulence verified in DNS implies novel control strategies