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

Abstract

The perspective of statistical state dynamics (SSD) has recently been applied to the study of mechanisms underlying turbulence in various physical systems. An example implementation of SSD is the second order closure referred to as stochastic structural stability theory (S3T), which has provided insight into the dynamics of wall turbulence and specifically the emergence and maintenance of the roll/streak structure. This closure eliminates nonlinear interactions among the perturbations has been removed, restricting nonlinearity in the dynamics to that of the mean equation and the interaction between the mean and perturbation covariance. Here, this quasi-linear restriction of the dynamics is used to study the structure and dynamics of turbulence in plane Poiseuille flow at moderately high Reynolds numbers in a closely related dynamical system, referred to as the restricted nonlinear (RNL) system. RNL simulations reveal that the essential features of wall-turbulence dynamics are retained. Remarkably, the RNL system spontaneously limits the support of its turbulence to a small set of streamwise Fourier components giving rise to a naturally minimal 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 a single streamwise component is imposed the RNL system continues to produce self-sustaining turbulent structure and dynamics. RNL turbulence at the Reynolds numbers studied is dominated by the roll/streak structure in the buffer layer and similar very-large-scale structure (VLSM) in the outer layer. Diagnostics of the structure, spectrum and energetics of RNL and DNS turbulence are used to demonstrate that the roll/streak dynamics supporting the turbulence in the buffer and logarithmic layer is essentially similar in RNL and DNS.

published in J. Fluid Mech., 26 pages, 15 figures. arXiv admin note: text overlap with arXiv:1401.7816

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Cited by in corpus (22)

• Coherent structures in wall-bounded turbulence
• Dynamo theories
• Bispectral mode decomposition of nonlinear flows
• Causality of energy-containing eddies in wall turbulence
• Non-equilibrium three-dimensional boundary layers at moderate Reynolds numbers
• Cause-and-effect of linear mechanisms sustaining wall turbulence
• Recent Developments in Theories of Inhomogeneous and Anisotropic Turbulence
• Nonlinear mechanism of the self-sustaining process in the buffer and logarithmic layer of wall-bounded flows
• A statistical state dynamics approach to wall-turbulence
• Generalised quasilinear approximations of turbulent channel flow: Part 1. Streamwise nonlinear energy transfer
• Instability of the roll/streak structure induced by free-stream turbulence in pre-transitional Couette flow
• Exploiting self-organized criticality in strongly stratified turbulence
• Generalised quasilinear approximations of turbulent channel flow: Part 2. Spanwise scale interactions
• Synchronization of Low Reynolds Number Plane Couette Turbulence
• Statistical state dynamics-based analysis of the physical mechanisms sustaining and regulating turbulence in Couette flow
• Improved assessment of the statistical stability of turbulent flows using extended Orr-Sommerfeld stability analysis
• Statistical state dynamics of weak jets in barotropic beta-plane turbulence
• Linear and nonlinear receptivity mechanisms in boundary layers subject to free-stream turbulence
• Threshold transient growth as a criterion for turbulent mean profiles
• The mechanism by which nonlinearity sustains turbulence in plane Couette flow
• Non-equivalence of quasilinear dynamical systems and their statistical closures
• Alternative physics to understand wall turbulence: Navier-Stokes equations with modified linear dynamics