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Register a new userPOD-based study of structure and dynamics in turbulent plane Poiseuille flow: comparing quasi-linear simulations to DNS
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Added by
Marios Andreas Nikolaidis
Publication date
2021
fields
Physics
and research's language is
English
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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.
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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 deep and unsolved problem of statistical physics whose solution requires to go beyond the assumption of a homogeneous and isotropic state, as fluctuations in turbulent flows are strongly related to the geometry of this flow. This links the dissipation to the space dependence of the average velocity field. Based on the idea that dissipation in fully developed turbulence is by singular events resulting from an evolution described by the Euler equations, it has been recently observed that the closure problem is strongly restricted, and that it implies that the turbulent stress is a non local function (in space) of the average velocity field, an extension of classical Boussinesq theory of turbulent viscosity. The resulting equations for the turbulent stress are derived here in one of the simplest possible physical situation, the turbulent Poiseuille flow between two parallel plates. In this case the integral kernel giving the turbulent stress, as function of the averaged velocity field, takes a simple form leading to a full analysis of the averaged turbulent flow in the limit of a very large Reynolds number. In this limit one has to match a viscous boundary layer, near the walls bounding the flow, and an outer solution in the bulk of the flow. This asymptotic analysis is non trivial because one has to match solution with logarithms. A non trivial and somewhat unexpected feature of this solution is that, besides the boundary layers close to the walls, there is another inner boundary layer near the center plane of the flow.
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.
A Direct Numerical Simulation (DNS) of the incompressible flow around a rectangular cylinder with chord-to-thickness ratio 5:1 (also known as the BARC benchmark) is presented. The work replicates the first DNS of this kind recently presented by Cimarelli et al (2018), and intends to contribute to a solid numerical benchmark, albeit at a relatively low value of the Reynolds number. The study differentiates from previous work by using an in-house finite-differences solver instead of the finite-volumes toolbox OpenFOAM, and by employing finer spatial discretization and longer temporal average. The main features of the flow are described, and quantitative differences with the existing results are highlighted. The complete set of terms appearing in the budget equation for the components of the Reynolds stress tensor is provided for the first time. The different regions of the flow where production, redistribution and dissipation of each component take place are identified, and the anisotropic and inhomogeneous nature of the flow is discussed. Such information is valuable for the verification and fine-tuning of turbulence models in this complex separating and reattaching flow.
This paper concerns the study of direct numerical simulation (DNS) data of a wavepacket in laminar turbulent transition in a Blasius boundary layer. The decomposition of this wavepacket into a set of modes (a basis that spans an approximate solution space) can be achieved in a wide variety of ways. Two well-known tools are the fast Fourier transform (FFT) and the proper orthogonal decomposition (POD). To synergize the strengths of both methods, a hybrid POD-FFT is pioneered, using the FFT as a tool for interpreting the POD modes. The POD-FFT automatically identifies well-known fundamental, subharmonic and Klebanoff modes in the flow, even though it is blind to the underlying physics. Moreover, the POD-FFT further separates the subharmonic content of the wavepacket into three fairly distinct parts: a positively detuned mode resembling a Lambda-vortex, a Craik-type tuned mode and a Herbert-type positive-negative detuned mode pair, in decreasing order of energy. This distinction is less widely recognized, but it provides a possible explanation for the slightly positively detuned subharmonic mode often observed in previous experiments and simulations.
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 following 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.
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