This paper describes a study of the self-sustaining process inwall-turbulence based on a second order statistical state dynamics (SSD) modelof Couette flow. SSD models with this form are referred to as S3T models andself-sustain turbulence with a mean flow and second order perturbationstructure similar to that obtained by DNS. The use of a SSD model to study thephysical mechanisms underlying turbulence has advantages over the traditionalapproach of studying the dynamics of individual realizations of turbulence. Oneadvantage is that the analytical structure of SSD isolates and directlyexpresses the interaction between the coherent mean flow and the incoherentperturbation components of the turbulence. Isolation of the interaction betweenthese components reveals how this interaction underlies both the maintenance ofthe turbulence variance by transfer of energy from the externally driven flowto the perturbation components as well as the enforcement of the observedstatistical mean turbulent state by feedback regulation between the mean andperturbation fields. Another advantage of studying turbulence using SSD modelsis that the analytical structure of S3T turbulence can be completelycharacterized. For example, turbulence in the S3T system is maintained by aparametric growth mechanism. Furthermore, the equilibrium statistical state ofthe turbulence can be demonstrated to be enforced by feedback regulation inwhich transient growth of the incoherent perturbations episodically suppressescoherent streak growth preventing runaway parametric growth of the incoherentturbulent component. Using S3T to isolate these parametric growth and feedbackregulation mechanisms allows a detailed characterization of the dynamics of theself-sustaining process in S3T turbulence with compelling implications forunderstanding the mechanism of wall-turbulence.
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