A statistical state dynamics-based study of the structure and mechanism of large-scale motions in plane Poiseuille flow

摘要

The perspective of statistical state dynamics (SSD) has recently been appliedto the study of mechanisms underlying turbulence in various physical systems.An example implementation of SSD is the second order closure referred to asstochastic structural stability theory (S3T), which has provided insight intothe dynamics of wall turbulence and specifically the emergence and maintenanceof the roll/streak structure. This closure eliminates nonlinear interactionsamong the perturbations has been removed, restricting nonlinearity in thedynamics to that of the mean equation and the interaction between the mean andperturbation covariance. Here, this quasi-linear restriction of the dynamics isused to study the structure and dynamics of turbulence in plane Poiseuille flowat moderately high Reynolds numbers in a closely related dynamical system,referred to as the restricted nonlinear (RNL) system. RNL simulations revealthat the essential features of wall-turbulence dynamics are retained.Remarkably, the RNL system spontaneously limits the support of its turbulenceto a small set of streamwise Fourier components giving rise to a naturallyminimal representation of its turbulence dynamics. Although greatly simplified,this RNL turbulence exhibits natural-looking structures and statistics.Surprisingly, even when further truncation of the perturbation support to asingle streamwise component is imposed the RNL system continues to produceself-sustaining turbulent structure and dynamics. RNL turbulence at theReynolds numbers studied is dominated by the roll/streak structure in thebuffer layer and similar very-large-scale structure (VLSM) in the outer layer.Diagnostics of the structure, spectrum and energetics of RNL and DNS turbulenceare used to demonstrate that the roll/streak dynamics supporting the turbulencein the buffer and logarithmic layer is essentially similar in RNL and DNS.