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تسجيل مستخدم جديدA statistical state dynamics-based study of the structure and mechanism of large-scale motions in plane Poiseuille flow
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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.
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Turbulence structure in the quasi-linear restricted nonlinear (RNL) model is analyzed and compared with DNS of turbulent Poiseuille flow at Reynolds number R=1650. The turbulence structure is obtained by POD analysis of the two components of the flow
partition used in formulating the RNL model: the streamwise-mean flow and the associated perturbations. The dominant structures are found to be similar in RNL simulations and DNS despite the neglect of perturbation-perturbation nonlinearity in the RNL formulation. POD analysis of the streamwise-mean flow indicates that the dominant structure in both RNL and DNS is a coherent roll-streak structure in which the roll is collocated with the streak in a manner configured to reinforce the streak by the lift-up process. This mechanism of roll-streak maintenance accords with analytical predictions made using the second order statistical state dynamics (SSD) model, referred to as S3T, which shares with RNL the dynamical restriction of neglecting the perturbation-perturbation nonlinearity. POD analysis of perturbations from the streamwise-mean streak reveals that similar structures characterize these perturbations in both RNL and DNS. The perturbation to the low-speed streak POD are shown to have the form of oblique waves collocated with the streak that can be identified with optimally growing structures on the streak. Given that the mechanism sustaining turbulence in RNL has been analytically characterized, this close correspondence between the streamwise-mean and perturbation structures in RNL and DNS supports the conclusion that the self-sustaining mechanism in DNS is the same as that in RNL.
The convection velocity of localized wave packet in plane-Poiseuille flow is found to be determined by a solitary wave at the centerline of a downstream vortex dipole in its mean field after deducting the basic flow. The fluctuation component followi
ng the vortex dipole oscillates with a global frequency selected by the upstream marginal absolute instability, and propagates obeying the local dispersion relation of the mean flow. By applying localized initial disturbances, a nonzero wave-packet density is achieved at the threshold state, suggesting a first order transition.
The ultimate goal of a sound theory of turbulence in fluids is to close in a rational way the Reynolds equations, namely to express the time averaged turbulent stress tensor as a function of the time averaged velocity field. This closure problem is a
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