Coherent structures, uniform momentum zones and the streamwise energy spectrum in wall-bounded turbulent flows

2017 ◽  
Vol 826 ◽  
Author(s):  
Theresa Saxton-Fox ◽  
Beverley J. McKeon
Keyword(s):  
Energy Spectrum ◽  
Velocity Field ◽  
Turbulent Flows ◽  
Coherent Structures ◽  
Large Scale ◽  
Stokes Equations ◽  
Structural Features ◽  
Travelling Wave ◽  
Spectral Signature ◽  
Representative Model

Large-scale motions (LSMs) in wall-bounded turbulent flows have well-characterised instantaneous structural features (Kovasznay et al., J. Fluid Mech., vol. 41 (2), 1970, pp. 283–325; Meinhart & Adrian, Phys. Fluids, vol. 7 (4), 1995, pp. 694–696) and a known spectral signature (Monty et al., J. Fluid Mech., vol. 632, 2009, pp. 431–442). This work aims to connect these previous observations through the development and analysis of a representative model for LSMs. The model is constructed to be consistent with the streamwise energy spectrum (Monty et al. 2009) and amplification characteristics of the Navier–Stokes equations (McKeon & Sharma, J. Fluid Mech., vol. 658, 2010, pp. 336–382), and is found to naturally recreate characteristics of instantaneous turbulent structures, including a bulge shape (Kovasznay et al. 1970) and the presence of uniform momentum zones (Meinhart & Adrian 1995) in the streamwise velocity field. The observed structural similarity between the LSM representative model and instantaneous experimental data supports the use of travelling wave models to connect statistical and instantaneous descriptions of coherent structures, and clarifies a simple general equivalency between symmetry in a Reynolds-decomposed velocity field and asymmetry in the laboratory frame.

Exact Coherent States and the Nonlinear Dynamics of Wall-Bounded Turbulent Flows

2021 ◽  
Vol 53 (1) ◽  
pp. 227-253 ◽  
Author(s):  
Michael D. Graham ◽  
Daniel Floryan
Keyword(s):  
State Space ◽  
Turbulent Flows ◽  
Coherent Structures ◽  
Coherent States ◽  
Large Scale ◽  
Stokes Equations ◽  
Saddle Points ◽  
Transport Processes ◽  
Hairpin Vortices ◽  
Theoretical Approaches

Wall-bounded turbulence exhibits patterns that persist in time and space: coherent structures. These are important for transport processes and form a conceptual framework for important theoretical approaches. Key observed structures include quasi-streamwise and hairpin vortices, as well as the localized spots and puffs of turbulence observed during transition. This review describes recent research on so-called exact coherent states (ECS) in wall-bounded parallel flows at Reynolds numbers Re [Formula: see text] 104; these are nonturbulent, nonlinear solutions to the Navier–Stokes equations that in many cases resemble coherent structures in turbulence. That is, idealized versions of many of these structures exist as distinct, self-sustaining entities. ECS are saddle points in state space and form, at least in part, the state space skeleton of the turbulent dynamics. While most work on ECS focuses on Newtonian flow, some advances have been made on the role of ECS in turbulent drag reduction in polymer solutions. Emerging directions include applications to control and connections to large-scale structures and the attached eddy model.

Characterization of Geometrical and Temporal Properties of Large-scale Motions in Turbulent Flows

2021 ◽  
Author(s):  
Christina Tsai ◽  
Kuang-Ting Wu
Keyword(s):  
Turbulent Flow ◽  
Turbulent Flows ◽  
Coherent Structures ◽  
Large Scale ◽  
Streamwise Velocity ◽  
Turbulent Structures ◽  
Temporal Properties ◽  
Turbulent Statistics ◽  
Spatial Locations

<p>It is demonstrated that turbulent boundary layers are populated by a hierarchy of recurrent structures, normally referred to as the coherent structures. Thus, it is desirable to gain a better understanding of the spatial-temporal characteristics of coherent structures and their impact on fluid particles. Furthermore, the ejection and sweep events play an important role in turbulent statistics. Therefore, this study focuses on the characterizations of flow particles under the influence of the above-mentioned two structures.</p><div><span>With regard to the geometry of turbulent structures, </span><span>Meinhart & Adrian (1995) </span>first highlighted the existence of large and irregularly shaped regions of uniform streamwise momentum zone (hereafter referred to as a uniform momentum zone, or UMZs), regions of relatively similar streamwise velocity with coherence in the streamwise and wall-normal directions.  <span>Subsequently, </span><span>de Silva et al. (2017) </span><span>provided a detection criterion that had previously been utilized to locate the uniform momentum zones (UMZ) and demonstrated the application of this criterion to estimate the spatial locations of the edges that demarcates UMZs.</span></div><div> </div><div>In this study, detection of the existence of UMZs is a pre-process of identifying the coherent structures. After the edges of UMZs are determined, the identification procedure of ejection and sweep events from turbulent flow DNS data should be defined. As such, an integrated criterion of distinguishing ejection and sweep events is proposed. Based on the integrated criterion, the statistical characterizations of coherent structures from available turbulent flow data such as event durations, event maximum heights, and wall-normal and streamwise lengths can be presented.</div>

scholarly journals Coherent structures in the linearized impulse response of turbulent channel flow

2019 ◽  
Vol 863 ◽  
pp. 1190-1203 ◽  
Author(s):  
Sabarish B. Vadarevu ◽  
Sean Symon ◽  
Simon J. Illingworth ◽  
Ivan Marusic
Keyword(s):  
Channel Flow ◽  
Coherent Structures ◽  
Large Scale ◽  
Body Force ◽  
Stokes Equations ◽  
Turbulent Channel Flow ◽  
Kinetic Energy Density ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Velocity Fluctuations

We study the evolution of velocity fluctuations due to an isolated spatio-temporal impulse using the linearized Navier–Stokes equations. The impulse is introduced as an external body force in incompressible channel flow at $Re_{\unicode[STIX]{x1D70F}}=10\,000$. Velocity fluctuations are defined about the turbulent mean velocity profile. A turbulent eddy viscosity is added to the equations to fix the mean velocity as an exact solution, which also serves to model the dissipative effects of the background turbulence on large-scale fluctuations. An impulsive body force produces flow fields that evolve into coherent structures containing long streamwise velocity streaks that are flanked by quasi-streamwise vortices; some of these impulses produce hairpin vortices. As these vortex–streak structures evolve, they grow in size to be nominally self-similar geometrically with an aspect ratio (streamwise to wall-normal) of approximately 10, while their kinetic energy density decays monotonically. The topology of the vortex–streak structures is not sensitive to the location of the impulse, but is dependent on the direction of the impulsive body force. All of these vortex–streak structures are attached to the wall, and their Reynolds stresses collapse when scaled by distance from the wall, consistent with Townsend’s attached-eddy hypothesis.

scholarly journals Examination of large-scale structures in a turbulent plane mixing layer. Part 2. Dynamical systems model

2001 ◽  
Vol 441 ◽  
pp. 67-108 ◽  
Author(s):  
L. UKEILEY ◽  
L. CORDIER ◽  
R. MANCEAU ◽  
J. DELVILLE ◽  
M. GLAUSER ◽  
...  
Keyword(s):  
Dynamical System ◽  
Velocity Field ◽  
Large Scale ◽  
Stokes Equations ◽  
Temporal Dynamics ◽  
Mixing Layer ◽  
Basis Set ◽  
Large Scale Structures ◽  
Scale Structures ◽  
Low Order

The temporal dynamics of large-scale structures in a plane turbulent mixing layer are studied through the development of a low-order dynamical system of ordinary differential equations (ODEs). This model is derived by projecting Navier–Stokes equations onto an empirical basis set from the proper orthogonal decomposition (POD) using a Galerkin method. To obtain this low-dimensional set of equations, a truncation is performed that only includes the first POD mode for selected streamwise/spanwise (k1/k3) modes. The initial truncations are for k3 = 0; however, once these truncations are evaluated, non-zero spanwise wavenumbers are added. These truncated systems of equations are then examined in the pseudo-Fourier space in which they are solved and by reconstructing the velocity field. Two different methods for closing the mean streamwise velocity are evaluated that show the importance of introducing, into the low-order dynamical system, a term allowing feedback between the turbulent and mean flows. The results of the numerical simulations show a strongly periodic flow indicative of the spanwise vorticity. The simulated flow had the correct energy distributions in the cross-stream direction. These models also indicated that the events associated with the centre of the mixing layer lead the temporal dynamics. For truncations involving both spanwise and streamwise wavenumbers, the reconstructed velocity field exhibits the main spanwise and streamwise vortical structures known to exist in this flow. The streamwise aligned vorticity is shown to connect spanwise vortex tubes.

scholarly journals On the analysis of a geometrically selective turbulence model

2020 ◽  
Vol 9 (1) ◽  
pp. 1402-1419 ◽  
Author(s):  
Nejmeddine Chorfi ◽  
Mohamed Abdelwahed ◽  
Luigi C. Berselli
Keyword(s):  
Turbulent Flows ◽  
Turbulence Model ◽  
Large Scale ◽  
Stokes Equations ◽  
A Priori ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Smagorinsky Model ◽  
Navier Stokes Equations ◽  
Velocity Pressure

Abstract In this paper we propose some new non-uniformly-elliptic/damping regularizations of the Navier-Stokes equations, with particular emphasis on the behavior of the vorticity. We consider regularized systems which are inspired by the Baldwin-Lomax and by the selective Smagorinsky model based on vorticity angles, and which can be interpreted as Large Scale methods for turbulent flows. We consider damping terms which are active at the level of the vorticity. We prove the main a priori estimates and compactness results which are needed to show existence of weak and/or strong solutions, both in velocity/pressure and velocity/vorticity formulation for various systems. We start with variants of the known ones, going later on to analyze the new proposed models.

Studying turbulence using direct numerical simulation: 1987 Center for Turbulence Research NASA Ames/Stanford Summer Programme

1988 ◽  
Vol 190 ◽  
pp. 375-392 ◽  
Author(s):  
J. C. R. Hunt
Keyword(s):  
Boundary Layers ◽  
Turbulent Flows ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Turbulent Boundary Layers ◽  
Finite Amplitude ◽  
Wall Layer ◽  
Navier Stokes ◽  
Scale Motion

This paper is an account of a summer programme for the study of the ideas and models of turbulent flows, using the results of direct numerical stimulations of the Navier-Stokes equations. These results had been obtained on the computers and stored as accessible databases at the Center for Turbulence Research (CTR) of NASA Ames Research Center and Stanford University. At this first summer programme, some 32 visiting researchers joined those at the CTR to test hypotheses and models in five aspects of turbulence research: turbulence decomposition, bifurcation and chaos; two-point closure (or k-space) modelling; structure of turbulent boundary layers; Reynolds-stress modelling; scalar transport and reacting flows.A number of new results emerged including: computation of space and space-time correlations in isotropic turbulence can be related to each other and modelled in terms of the advection of small scales by large-scale motion; the wall layer in turbulent boundary layers is dominated by shear layers which protrude into the outer layers, and have long lifetimes; some aspects of the ejection mechanism for these layers can be described in terms of the two-dimensional finite-amplitude Navier-Stokes solutions; a self-similar form of the two-point, cross-correlation data of the turbulence in boundary layers (when normalized by the r.m.s. value at the furthest point from the wall) shows how both the blocking of eddies by the wall and straining by the mean shear control the lengthscales; the intercomponent transfer (pressure-strain) is highly localized in space, usually in regions of concentrated vorticity; conditioned pressure gradients are linear in the conditioning of velocity and independent of vorticity in homogeneous shear flow; some features of coherent structures in the boundary layer are similar to experimental measurements of structures in mixing-layers, jets and wakes.The availability of comprehensive velocity and pressure data certainly helps the investigation of concepts and models. But a striking feature of the summer programme was the diversity of interpretation of the same computed velocity fields. There are few signs of any convergence in turbulence research! But with new computational facilities the divergent approaches can at least be related to each other.

Active Control of Near-Wall Coherent Structures

2002 ◽  
Author(s):  
P. Konieczny ◽  
A. Bottaro ◽  
V. Monturet ◽  
B. Nogarede
Keyword(s):  
Boundary Layer ◽  
Skin Friction ◽  
Coherent Structures ◽  
Large Scale ◽  
Travelling Wave ◽  
Friction Reduction ◽  
Wall Turbulence ◽  
Integral Control ◽  
Macroscopic Simulation ◽  
Near Wall

This work aims at finding efficient means to reduce skin friction drag in a turbulent boundary layer. The argument on which the study is based is that turbulence exists near a wall because of the presence of an autonomous cycle which is maintained even in the absence of forcing from the free-stream. The central elements of this cycle are the near-wall coherent structures whose dynamics control the turbulence production. It is postulated that an action at the wall capable of disrupting the turbulent wall-cycle can yield a significant skin friction reduction. A model cycle is produced by embedding artificial, large scale streamwise vortices and streaks in a Blasius boundary layer. A control is then conceived, meant to produce an agglomeration of the streaks to hamper the cycle. The action envisaged consists in a movement of the wall, in the form of a spanwise standing or travelling wave of sufficiently long wavelength. The controllers in the present macroscopic simulation are simply cantilever beams whose movement is driven by ceramic piezo-actuators. Piezoelectric fibers realizing the same action (properly rescaled) provide, possibly, the answer to the technological challenge of the integral control of near-wall turbulence.

scholarly journals Turbulent 2.5-dimensional dynamos

2016 ◽  
Vol 799 ◽  
pp. 246-264 ◽  
Author(s):  
K. Seshasayanan ◽  
A. Alexakis
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Two Dimensional Flow

We study the linear stage of the dynamo instability of a turbulent two-dimensional flow with three components $(u(x,y,t),v(x,y,t),w(x,y,t))$ that is sometimes referred to as a 2.5-dimensional (2.5-D) flow. The flow evolves based on the two-dimensional Navier–Stokes equations in the presence of a large-scale drag force that leads to the steady state of a turbulent inverse cascade. These flows provide an approximation to very fast rotating flows often observed in nature. The low dimensionality of the system allows for the realization of a large number of numerical simulations and thus the investigation of a wide range of fluid Reynolds numbers $Re$, magnetic Reynolds numbers $Rm$ and forcing length scales. This allows for the examination of dynamo properties at different limits that cannot be achieved with three-dimensional simulations. We examine dynamos for both large and small magnetic Prandtl-number turbulent flows $Pm=Rm/Re$, close to and away from the dynamo onset, as well as dynamos in the presence of scale separation. In particular, we determine the properties of the dynamo onset as a function of $Re$ and the asymptotic behaviour in the large $Rm$ limit. We are thus able to give a complete description of the dynamo properties of these turbulent 2.5-D flows.

Self-conditioned fields for large-eddy simulations of turbulent flows

2010 ◽  
Vol 652 ◽  
pp. 139-169 ◽  
Author(s):  
STEPHEN B. POPE
Keyword(s):  
Velocity Field ◽  
Density Function ◽  
Turbulent Flows ◽  
Evolution Equations ◽  
Stokes Equations ◽  
The Self ◽  
Mean Velocity ◽  
Full Account ◽  
Filtered Density Function ◽  
Large Eddy

An alternative foundation is developed for the large-eddy simulation (LES) of turbulent flows. It is based on ‘self-conditioned fields’, for example, the mean velocity field conditional on a discrete representation of the filtered velocity field. It is shown that the self-conditioned velocity field minimizes the residual kinetic energy, and that, with the ideal model, the method yields the correct one-time behaviour as determined by the Navier–Stokes equations. The approach is extended to the self-conditioned probability density function (PDF) of compositions. Compared to LES formulations based on the filtered velocity and the filtered density function, the self-conditioned field approach has several advantages: for laminar flow, and in the direct-numerical-simulation limit, the residual fluctuations are zero or exponentially small; full account is taken of the probability distribution of turbulent fields; there are no commutation issues; and there are no issues with filtering at walls, where the self-conditioned velocity is zero. The exact evolution equations for the self-conditioned velocity and composition PDF are derived. Basic models are presented, and the development of improved models is discussed.

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