scholarly journals A statistical state dynamics approach to wall turbulence

2017 ◽  
Vol 375 (2089) ◽  
pp. 20160081 ◽  
Author(s):  
B. F. Farrell ◽  
D. F. Gayme ◽  
P. J. Ioannou
Keyword(s):  
Wall Turbulence ◽  
Large Reynolds Number ◽  
Perturbation Equation ◽  
Computationally Efficient ◽  
Mean Flow ◽  
Computational Tools ◽  
Statistical State ◽  
Quantitative Accuracy ◽  
The Mean ◽  
Selection Of

This paper reviews results obtained using statistical state dynamics (SSD) that demonstrate the benefits of adopting this perspective for understanding turbulence in wall-bounded shear flows. The SSD approach used in this work employs a second-order closure that retains only the interaction between the streamwise mean flow and the streamwise mean perturbation covariance. This closure restricts nonlinearity in the SSD to that explicitly retained in the streamwise constant mean flow together with nonlinear interactions between the mean flow and the perturbation covariance. This dynamical restriction, in which explicit perturbation–perturbation nonlinearity is removed from the perturbation equation, results in a simplified dynamics referred to as the restricted nonlinear (RNL) dynamics. RNL systems, in which a finite ensemble of realizations of the perturbation equation share the same mean flow, provide tractable approximations to the SSD, which is equivalent to an infinite ensemble RNL system. This infinite ensemble system, referred to as the stochastic structural stability theory system, introduces new analysis tools for studying turbulence. RNL systems provide computationally efficient means to approximate the SSD and produce self-sustaining turbulence exhibiting qualitative features similar to those observed in direct numerical simulations despite greatly simplified dynamics. The results presented show that RNL turbulence can be supported by as few as a single streamwise varying component interacting with the streamwise constant mean flow and that judicious selection of this truncated support or ‘band-limiting’ can be used to improve quantitative accuracy of RNL turbulence. These results suggest that the SSD approach provides new analytical and computational tools that allow new insights into wall turbulence. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

scholarly journals Statistical evidence of anasymptotic geometric structure to the momentum transporting motions in turbulent boundary layers

2017 ◽  
Vol 375 (2089) ◽  
pp. 20160084 ◽  
Author(s):  
Caleb Morrill-Winter ◽  
Jimmy Philip ◽  
Joseph Klewicki
Keyword(s):  
Boundary Layers ◽  
Reynolds Shear Stress ◽  
Turbulent Boundary Layers ◽  
Wall Turbulence ◽  
Sensor Data ◽  
Joint Analysis ◽  
Large Reynolds Number ◽  
Mean Flow ◽  
Length Scales ◽  
The Mean

The turbulence contribution to the mean flow is reflected by the motions producing the Reynolds shear stress (〈− uv 〉) and its gradient. Recent analyses of the mean dynamical equation, along with data, evidence that these motions asymptotically exhibit self-similar geometric properties. This study discerns additional properties associated with the uv signal, with an emphasis on the magnitudes and length scales of its negative contributions. The signals analysed derive from high-resolution multi-wire hot-wire sensor data acquired in flat-plate turbulent boundary layers. Space-filling properties of the present signals are shown to reinforce previous observations, while the skewness of uv suggests a connection between the size and magnitude of the negative excursions on the inertial domain. Here, the size and length scales of the negative uv motions are shown to increase with distance from the wall, whereas their occurrences decrease. A joint analysis of the signal magnitudes and their corresponding lengths reveals that the length scales that contribute most to 〈− uv 〉 are distinctly larger than the average geometric size of the negative uv motions. Co-spectra of the streamwise and wall-normal velocities, however, are shown to exhibit invariance across the inertial region when their wavelengths are normalized by the width distribution, W ( y ), of the scaling layer hierarchy, which renders the mean momentum equation invariant on the inertial domain. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

Orientation and rotation of inertial disk particles in wall turbulence

2015 ◽  
Vol 766 ◽  
Author(s):  
Niranjan Reddy Challabotla ◽  
Lihao Zhao ◽  
Helge I. Andersson
Keyword(s):  
Translational Motion ◽  
Turbulent Channel Flow ◽  
Stokes Number ◽  
Wall Turbulence ◽  
Rotational Inertia ◽  
Inertial Particles ◽  
Mean Flow ◽  
Flow Vorticity ◽  
Oblate Spheroids ◽  
The Mean

AbstractThe translational and rotational dynamics of oblate spheroidal particles suspended in a directly simulated turbulent channel flow have been examined. Inertial disk-like particles exhibited a significant preferential orientation in the plane of the mean shear. The rotational inertia about the symmetry axis of the disk-like particles hampered the spin-up of the flattest particles to match the mean flow vorticity. The influence of the particle shape on the orientation and rotation diminished as the translational inertia increased from Stokes number 1 to 30. An isotropization of both orientation and rotation could be observed in the core region of the channel. The translational motion of the oblate spheroids had a weak dependence on the aspect ratio. We therefore concluded that inertial particles sample nearly the same flow field irrespective of shape. Nevertheless, the orientation and rotation of disk-like particles turned out to be qualitatively different from the dynamics of fibre-like particles.

An experimental study of the turbulence structure in smooth- and rough-wall boundary layers

1987 ◽  
Vol 177 ◽  
pp. 437-466 ◽  
Author(s):  
A. E. Perry ◽  
K. L. Lim ◽  
S. M. Henbest
Keyword(s):  
Boundary Layers ◽  
Wall Turbulence ◽  
Wall Region ◽  
Turbulence Structure ◽  
Hot Wire ◽  
Mean Flow ◽  
Wavy Surfaces ◽  
The Mean ◽  
Flow Turbulence ◽  
Turbulent Wall

The turbulence structure in zero-pressure-gradient boundary layers above smooth, rough and wavy surfaces was investigated. The mean flow, turbulence intensity and spectral data for both smooth and rough surfaces show support for the attached eddy hypothesis of Townsend (1976), the model for wall turbulence proposed by Perry & Chong (1982) and the extended version developed by Perry, Henbest & Chong (1986). Anomalies in hot-wire behaviour when measuring in the turbulent wall region of the flow were discovered and some of these have been resolved.

Direct numerical simulation of turbulent duct flow with inclined or V-shaped ribs mounted on one wall

2021 ◽  
Vol 932 ◽  
Author(s):  
S.V. Mahmoodi-Jezeh ◽  
Bing-Chen Wang
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Secondary Flows ◽  
Wall Turbulence ◽  
Spanwise Direction ◽  
Duct Flow ◽  
Mean Flow ◽  
Square Duct ◽  
Turbulence Structures ◽  
The Mean

In this research, highly disturbed turbulent flow of distinct three-dimensional characteristics in a square duct with inclined or V-shaped ribs mounted on one wall is investigated using direct numerical simulation. The turbulence field is highly sensitive to not only the rib geometry but also the boundary layers developed over the side and top walls. In a cross-stream plane secondary flows appear as large longitudinal vortices in both inclined and V-shaped rib cases due to the confinement of four sidewalls of the square duct. However, owing to the difference in the pattern of cross-stream secondary flow motions, the flow physics is significantly different in these two ribbed duct cases. It is observed that the mean flow structures in the cross-stream directions are asymmetrical in the inclined rib case but symmetrical in the V-shaped rib case, causing substantial differences in the momentum transfer across the spanwise direction. The impacts of rib geometry on near-wall turbulence structures are investigated using vortex identifiers, joint probability density functions between the streamwise and vertical velocity fluctuations, statistical moments of different orders, spatial two-point autocorrelations and velocity spectra. It is found that near the leeward and windward rib faces, the mean inclination angle of turbulence structures in the V-shaped rib case is greater than that of the inclined rib case, which subsequently enhances momentum transport between the ribbed bottom wall and the smooth top wall.

scholarly journals Restricted nonlinear model for high- and low-drag events in plane channel flow

2019 ◽  
Vol 864 ◽  
pp. 221-243 ◽  
Author(s):  
Frédéric Alizard ◽  
Damien Biau
Keyword(s):  
Channel Flow ◽  
Plane Channel ◽  
Wall Turbulence ◽  
Asymptotic State ◽  
State Variables ◽  
Mean Flow ◽  
Quadratic Interaction ◽  
Maximum Drag Reduction ◽  
The Mean ◽  
Plane Channel Flow

A restricted nonlinear (RNL) model, obtained by partitioning the state variables into streamwise-averaged quantities and superimposed perturbations, is used in order to track the exact coherent state in plane channel flow investigated by Toh & Itano (J. Fluid Mech., vol. 481, 2003, pp. 67–76). When restricting nonlinearities to quadratic interaction of the fluctuating part into the streamwise-averaged component, it is shown that the coherent structure and its dynamics closely match results from direct numerical simulation (DNS), even if only a single streamwise Fourier mode is retained. In particular, both solutions exhibit long quiescent phases, spanwise shifts and bursting events. It is also shown that the dynamical trajectory passes close to equilibria that exhibit either low- or high-drag states. When statistics are collected at times where the friction velocity peaks, the mean flow and root-mean-square profiles show the essential features of wall turbulence obtained by DNS for the same friction Reynolds number. For low-drag events, the mean flow profiles are related to a universal asymptotic state called maximum drag reduction (Xi & Graham, Phys. Rev. Lett., vol. 108, 2012, 028301). Hence, the intermittent nature of self-sustaining processes in the buffer layer is contained in the dynamics of the RNL model, organized in two exact coherent states plus an asymptotic turbulent-like attractor. We also address how closely turbulent dynamics approaches these equilibria by exploiting a DNS database associated with a larger domain.

scholarly journals Modulation of near-wall turbulence in the transitionally rough regime

2019 ◽  
Vol 865 ◽  
pp. 1042-1071 ◽  
Author(s):  
Nabil Abderrahaman-Elena ◽  
Chris T. Fairhall ◽  
Ricardo García-Mayoral
Keyword(s):  
Shear Flow ◽  
Flow Instability ◽  
Direct Numerical Simulations ◽  
Wall Turbulence ◽  
Mean Flow ◽  
Displacement Height ◽  
Background Turbulence ◽  
The Mean ◽  
Shear Flow Instability ◽  
Near Wall Turbulence

Direct numerical simulations of turbulent channels with rough walls are conducted in the transitionally rough regime. The effect that roughness produces on the overlying turbulence is studied using a modified triple decomposition of the flow. This decomposition separates the roughness-induced contribution from the background turbulence, with the latter essentially free of any texture footprint. For small roughness, the background turbulence is not significantly altered, but merely displaced closer to the roughness crests, with the change in drag being proportional to this displacement. As the roughness size increases, the background turbulence begins to be modified, notably by the increase of energy for short, wide wavelengths, which is consistent with the appearance of a shear-flow instability of the mean flow. A laminar model is presented to estimate the roughness-coherent contribution, as well as the displacement height and the velocity at the roughness crests. Based on the effects observed in the background turbulence, the roughness function is decomposed into different terms to analyse different contributions to the change in drag, laying the foundations for a predictive model.

scholarly journals Self-sustaining processes at all scales in wall-bounded turbulent shear flows

2017 ◽  
Vol 375 (2089) ◽  
pp. 20160088 ◽  
Author(s):  
Carlo Cossu ◽  
Yongyun Hwang
Keyword(s):  
Large Scale ◽  
Shear Flows ◽  
Stokes Equations ◽  
Wall Turbulence ◽  
Turbulent Shear ◽  
Large Reynolds Number ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Full Account ◽  
Turbulent Shear Flows

We collect and discuss the results of our recent studies which show evidence of the existence of a whole family of self-sustaining motions in wall-bounded turbulent shear flows with scales ranging from those of buffer-layer streaks to those of large-scale and very-large-scale motions in the outer layer. The statistical and dynamical features of this family of self-sustaining motions, which are associated with streaks and quasi-streamwise vortices, are consistent with those of Townsend’s attached eddies. Motions at each relevant scale are able to sustain themselves in the absence of forcing from larger- or smaller-scale motions by extracting energy from the mean flow via a coherent lift-up effect. The coherent self-sustaining process is embedded in a set of invariant solutions of the filtered Navier–Stokes equations which take into full account the Reynolds stresses associated with the residual smaller-scale motions. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

Numerical Simulation of Internal Cavities Acoustic Trapped Modes With Mean Flow

2010 ◽  
Author(s):  
Kareem Aly ◽  
Samir Ziada
Keyword(s):  
Mach Number ◽  
Acoustic Field ◽  
Particle Velocity ◽  
Perturbation Equation ◽  
Duct System ◽  
Trapped Modes ◽  
Mean Flow ◽  
Phase Gradient ◽  
The Mean ◽  
Mach Numbers

Flow-excited acoustic resonance of trapped modes in ducts has been reported in different engineering applications. The excitation mechanism of these modes results from the interaction between the hydrodynamic flow field and the acoustic particle velocity, and is therefore dependent on the mode shape of the resonant acoustic field, including the amplitude and phase distributions of the acoustic particle velocity. For a cavity-duct system, the aerodynamic excitation of the trapped modes can generate strong pressure pulsations at moderate Mach numbers (M>0.1). This paper investigates numerically the effect of mean flow on the characteristics of the acoustic trapped modes for a cavity-duct system. Numerical simulations are performed for a two-dimensional planar configuration and different flow Mach numbers up to 0.3. A two-step numerical scheme is adopted in the investigation. A linearized acoustic perturbation equation is used to predict the acoustic field. The results show that as the Mach number is increased, the acoustic pressure distribution develops an axial phase gradient, but the shape of the amplitude distribution remains the same. Moreover, the amplitude and phase distributions of the acoustic particle velocity are found to change significantly near the cavity shear layer with the increase of the mean flow Mach number. These results demonstrate the importance of considering the effects of the mean flow on the flow-sound interaction mechanism.

scholarly journals Quantifying wall turbulence via a symmetry approach: a Lie group theory

2017 ◽  
Vol 827 ◽  
pp. 322-356 ◽  
Author(s):  
Zhen-Su She ◽  
Xi Chen ◽  
Fazle Hussain
Keyword(s):  
Lie Group ◽  
Group Analysis ◽  
Wall Turbulence ◽  
Length Function ◽  
Mean Flow ◽  
Mean Velocity ◽  
Group Invariance ◽  
The Mean ◽  
Dilatation Group ◽  
Analytical Expressions

First-principle-based prediction of mean-flow quantities of wall-bounded turbulent flows (channel, pipe and turbulent boundary layer (TBL)) is of great importance from both physics and engineering standpoints. Here we present a symmetry-based approach which yields analytical expressions for the mean-velocity profile (MVP) from a Lie-group analysis. After verifying the dilatation-group invariance of the Reynolds averaged Navier–Stokes (RANS) equation in the presence of a wall, we depart from previous Lie-group studies of wall turbulence by selecting a stress length function as a similarity variable. We argue that this stress length function characterizes the symmetry property of wall flows having a simple dilatation-invariant form. Three kinds of (local) invariant forms of the length function are postulated, a combination of which yields a multi-layer formula giving its distribution in the entire flow region normal to the wall and hence also the MVP, using the mean-momentum equation. In particular, based on this multi-layer formula, we obtain analytical expressions for the (universal) wall function and separate wake functions for pipe and channel, which are validated by data from direct numerical simulations (DNS). In conclusion, an analytical expression for the entire MVP of wall turbulence, beyond the log law or power law, is developed in this paper and the theory can be used to describe the mean turbulent kinetic-energy distribution, as well as a variety of boundary conditions such as pressure gradient, wall roughness, buoyancy, etc. where the dilatation-group invariance is valid in the wall-normal direction.

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

2016 ◽  
Vol 809 ◽  
pp. 290-315 ◽  
Author(s):  
Brian F. Farrell ◽  
Petros J. Ioannou ◽  
Javier Jiménez ◽  
Navid C. Constantinou ◽  
Adrián Lozano-Durán ◽  
...  
Keyword(s):  
Dynamical System ◽  
Poiseuille Flow ◽  
Large Scale ◽  
Dynamic Properties ◽  
Reynolds Numbers ◽  
Wall Turbulence ◽  
Plane Poiseuille Flow ◽  
Statistical State ◽  
The Mean ◽  
High Reynolds

The perspective of statistical state dynamics (SSD) has recently been applied to the study of mechanisms underlying turbulence in a variety of physical systems. An SSD is a dynamical system that evolves a representation of the statistical state of the system. An example of an SSD is the second-order cumulant 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. S3T comprises a coupled set of equations for the streamwise mean and perturbation covariance, in which 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. In this work, 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. Simulations using this RNL system reveal that the essential features of wall-turbulence dynamics are retained. Consistent with previous analyses based on the S3T version of SSD, 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, albeit with quantitative differences from those in direct numerical simulations (DNS) of the full equations. Surprisingly, even when further truncation of the perturbation support to a single streamwise component is imposed, the RNL system continues to self-sustain turbulence with qualitatively realistic structure and dynamic properties. 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. In this work, 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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