Spatial organization of large- and very-large-scale motions in a turbulent channel flow

2014 ◽  
Vol 749 ◽  
pp. 818-840 ◽  
Author(s):  
Jin Lee ◽  
Jae Hwa Lee ◽  
Jung-Il Choi ◽  
Hyung Jin Sung
Keyword(s):  
Channel Flow ◽  
Large Scale ◽  
Spatial Organization ◽  
Outer Region ◽  
Turbulent Channel Flow ◽  
Streamwise Velocity ◽  
Velocity Fluctuations ◽  
Spatial Features ◽  
Temporal Features ◽  
Low Speed Streaks

AbstractDirect numerical simulations were carried out to investigate the spatial features of large- and very-large-scale motions (LSMs and VLSMs) in a turbulent channel flow ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Re}_{\tau }=930$). A streak detection method based on the streamwise velocity fluctuations was used to individually trace the cores of LSMs and VLSMs. We found that both the LSM and VLSM populations were large. Several of the wall-attached LSMs stretched toward the outer regions of the channel. The VLSMs consisted of inclined outer LSMs and near-wall streaks. The number of outer LSMs increased linearly with the streamwise length of the VLSMs. The temporal features of the low-speed streaks in the outer region revealed that growing and merging events dominated the large-scale (1–$3\delta $) structures. The VLSMs $({>}3\delta )$ were primarily created by merging events, and the statistical analysis of these events supported that the merging of large-scale upstream structures contributed to the formation of VLSMs. Because the local convection velocity is proportional to the streamwise velocity fluctuations, the streamwise-aligned structures of the positive- and negative-$u$ patches suggested a primary mechanism underlying the merging events. The alignment of the positive- and negative-$u$ structures may be an essential prerequisite for the formation of VLSMs.

Large-scale structures in a turbulent channel flow with a minimal streamwise flow unit

2018 ◽  
Vol 850 ◽  
pp. 733-768 ◽  
Author(s):  
Hiroyuki Abe ◽  
Robert Anthony Antonia ◽  
Sadayoshi Toh
Keyword(s):  
Channel Flow ◽  
Velocity Fluctuation ◽  
Large Scale ◽  
Outer Region ◽  
Turbulent Channel Flow ◽  
Streamwise Velocity ◽  
Flow Unit ◽  
Wall Turbulence ◽  
Large Scale Structures ◽  
Scale Structures

Direct numerical simulations are used to examine large-scale motions with a streamwise length$2\sim 4h$($h$denotes the channel half-width) in the logarithmic and outer regions of a turbulent channel flow. We test a minimal ‘streamwise’ flow unit (Toh & Itano,J. Fluid Mech., vol. 524, 2005, pp. 249–262) (or MSU) for larger Kármán numbers ($h^{+}=395$and 1020) than in the original work. This flow unit consists of a sufficiently long (${L_{x}}^{+}\approx 400$) streamwise domain to maintain near-wall turbulence (Jiménez & Moin,J. Fluid Mech., vol. 225, 1991, pp. 213–240) and a spanwise domain which is large enough to represent the spanwise behaviour of inner and outer structures correctly; as$h^{+}$increases, the streamwise extent of the MSU domain decreases with respect to$h$. Particular attention is given to whether the spanwise organization of the large-scale structures may be represented properly in this simplified system at sufficiently large$h^{+}$and how these structures are associated with the mean streamwise velocity$\overline{U}$. It is shown that, in the MSU, the large-scale structures become approximately two-dimensional at$h^{+}=1020$. In this case, the streamwise velocity fluctuation$u$is energized, whereas the spanwise velocity fluctuation$w$is weakened significantly. Indeed, there is a reduced energy redistribution arising from the impaired global nature of the pressure, which is linked to the reduced linear–nonlinear interaction in the Poisson equation (i.e. the rapid pressure). The logarithmic dependence of$\overline{ww}$is also more evident due to the reduced large-scale spanwise meandering. On the other hand, the spanwise organization of the large-scale$u$structures is essentially identical for the MSU and large streamwise domain (LSD). One discernible difference, relative to the LSD, is that the large-scale structures in the MSU are more energized in the outer region due to a reduced turbulent diffusion. In this region, there is a tight coupling between neighbouring structures, which yields antisymmetric pairs (with respect to centreline) of large-scale structures with a spanwise spacing of approximately$3h$; this is intrinsically identical with the outer energetic mode in the optimal transient growth of perturbations (del Álamo & Jiménez,J. Fluid Mech., vol. 561, 2006, pp. 329–358).

Inner–outer interactions of large-scale structures in turbulent channel flow

2016 ◽  
Vol 790 ◽  
pp. 128-157 ◽  
Author(s):  
Jinyul Hwang ◽  
Jin Lee ◽  
Hyung Jin Sung ◽  
Tamer A. Zaki
Keyword(s):  
Channel Flow ◽  
High Speed ◽  
Large Scale ◽  
Spatial Coherence ◽  
Turbulent Channel Flow ◽  
Streamwise Velocity ◽  
Velocity Fluctuations ◽  
Merging Process ◽  
Convection Speed ◽  
Near Wall

Direct numerical simulation data of turbulent channel flow ($Re_{{\it\tau}}=930$) are used to investigate the statistics of long motions of streamwise velocity fluctuations ($u$), and the interaction of these structures with the near-wall disturbances, which is facilitated by their associated large-scale circulations. In the log layer, the negative-$u$ structures are organized into longer streamwise extent (${>}3{\it\delta}$) in comparison to the positive-$u$ counterparts. Near the wall, the footprint of negative-$u$ structures is relatively narrow in comparison to the footprint of positive-$u$ structures. This difference is due to the opposite spanwise motions in the vicinity of the footprints, which are either congregative or dispersive depending on the circulation of the outer roll cells. Conditional sampling of the footprints shows that the spanwise velocity fluctuations ($w$) are significantly enhanced by the dispersive motions of high-speed structures. On the other hand, the near-wall congregative motions of negative-$u$ structures generate relatively weak $w$ but intense negative-$u$ regions due, in part, to the spanwise collective migration of near-wall streaks. The concentrated near-wall regions of negative-$u$ upwell during the merging of the outer long scales – an effect that is demonstrated using statistical analysis of the merging process. This leads to a reduction of the convection speed of downstream negative-$u$ structures and thus promotes the merging with upstream ones. These top-down and bottom-up interactions enhance the spatial coherence of long negative-$u$ structures in the log region.

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 Streak instability in turbulent channel flow: the seeding mechanism of large-scale motions

2017 ◽  
Vol 832 ◽  
pp. 483-513 ◽  
Author(s):  
Matteo de Giovanetti ◽  
Hyung Jin Sung ◽  
Yongyun Hwang
Keyword(s):  
Channel Flow ◽  
Large Scale ◽  
Vortical Structure ◽  
Outer Region ◽  
Turbulent Channel Flow ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Hairpin Vortices ◽  
Large Scale Motion ◽  
Scale Motion

It has often been proposed that the formation of large-scale motion (or bulges) is a consequence of successive mergers and/or growth of near-wall hairpin vortices. In the present study, we report our direct observation that large-scale motion is generated by an instability of an ‘amplified’ streaky motion in the outer region (i.e. very-large-scale motion). We design a numerical experiment in turbulent channel flow up to $Re_{\unicode[STIX]{x1D70F}}\simeq 2000$ where a streamwise-uniform streaky motion is artificially driven by body forcing in the outer region computed from the previous linear theory (Hwang & Cossu, J. Fluid Mech., vol. 664, 2015, pp. 51–73). As the forcing amplitude is increased, it is found that an energetic streamwise vortical structure emerges at a streamwise wavelength of $\unicode[STIX]{x1D706}_{x}/h\simeq 1{-}5$ ($h$ is the half-height of the channel). The application of dynamic mode decomposition and the examination of turbulence statistics reveal that this structure is a consequence of the sinuous-mode instability of the streak, a subprocess of the self-sustaining mechanism of the large-scale outer structures. It is also found that the statistical features of the vortical structure are remarkably similar to those of the large-scale motion in the outer region. Finally, it is proposed that the largest streamwise length of the streak instability determines the streamwise length scale of very-large-scale motion.

scholarly journals Simultaneous Stereo PIV and MPS3 Wall-Shear Stress Measurements in Turbulent Channel Flow

Optics ◽  
2020 ◽  
Vol 1 (1) ◽  
pp. 40-51
Author(s):  
Esther Mäteling ◽  
Michael Klaas ◽  
Wolfgang Schröder
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Channel Flow ◽  
Inclination Angle ◽  
Large Scale ◽  
Turbulent Channel Flow ◽  
Two Dimensional ◽  
Velocity Fluctuations ◽  
Wall Shear ◽  
Near Wall

An extended experimental method is presented in which the micro-pillar shear-stress sensor (MPS 3 ) and high-speed stereo particle-image velocimetry measurements are simultaneously performed in turbulent channel flow to conduct concurrent time-resolved measurements of the two-dimensional wall-shear stress (WSS) distribution and the velocity field in the outer flow. The extended experimental setup, which involves a modified MPS 3 measurement setup and data evaluation compared to the standard method, is presented and used to investigate the footprint of the outer, large-scale motions (LSM) onto the near-wall small-scale motions. The measurements were performed in a fully developed, turbulent channel flow at a friction Reynolds number R e τ = 969 . A separation between large and small scales of the velocity fluctuations and the WSS fluctuations was performed by two-dimensional empirical mode decomposition. A subsequent cross-correlation analysis between the large-scale velocity fluctuations and the large-scale WSS fluctuations shows that the streamwise inclination angle between the LSM in the outer layer and the large-scale footprint imposed onto the near-wall dynamics has a mean value of Θ ¯ x = 16.53 ∘ , which is consistent with the literature relying on direct numerical simulations and hot-wire anemometry data. When also considering the spatial shift in the spanwise direction, the mean inclination angle reduces to Θ ¯ x z = 13.92 ∘ .

scholarly journals Statistics and structure of spanwise rotating turbulent channel flow at moderate Reynolds numbers

2017 ◽  
Vol 828 ◽  
pp. 424-458 ◽  
Author(s):  
Geert Brethouwer
Keyword(s):  
Reynolds Number ◽  
Channel Flow ◽  
Large Scale ◽  
Linear Part ◽  
Turbulent Channel Flow ◽  
Streamwise Velocity ◽  
Reynolds Stresses ◽  
System Rotation ◽  
The Mean ◽  
Spanwise Rotation

A study of fully developed plane turbulent channel flow subject to spanwise system rotation through direct numerical simulations is presented. In order to study both the influence of the Reynolds number and spanwise rotation on channel flow, the Reynolds number $Re=U_{b}h/\unicode[STIX]{x1D708}$ is varied from a low 3000 to a moderate 31 600 and the rotation number $Ro=2\unicode[STIX]{x1D6FA}h/U_{b}$ is varied from 0 to 2.7, where $U_{b}$ is the mean bulk velocity, $h$ the channel half-gap, $\unicode[STIX]{x1D708}$ the viscosity and $\unicode[STIX]{x1D6FA}$ the system rotation rate. The mean streamwise velocity profile displays also at higher $Re$ a characteristic linear part with a slope near to $2\unicode[STIX]{x1D6FA}$, and a corresponding linear part in the profiles of the production and dissipation rate of turbulent kinetic energy appears. With increasing $Ro$, a distinct unstable side with large spanwise and wall-normal Reynolds stresses and a stable side with much weaker turbulence develops in the channel. The flow starts to relaminarize on the stable side of the channel and persisting turbulent–laminar patterns appear at higher $Re$. If $Ro$ is further increased, the flow on the stable side becomes laminar-like while at yet higher $Ro$ the whole flow relaminarizes, although the calm periods might be disrupted by repeating bursts of turbulence, as explained by Brethouwer (Phys. Rev. Fluids, vol. 1, 2016, 054404). The influence of the Reynolds number is considerable, in particular on the stable side of the channel where velocity fluctuations are stronger and the flow relaminarizes less quickly at higher $Re$. Visualizations and statistics show that, at $Ro=0.15$ and 0.45, large-scale structures and large counter-rotating streamwise roll cells develop on the unstable side. These become less noticeable and eventually vanish when $Ro$ rises, especially at higher $Re$. At high $Ro$, the largest energetic structures are larger at lower $Re$.

The structure of the viscous sublayer and the adjacent wall region in a turbulent channel flow

1974 ◽  
Vol 65 (3) ◽  
pp. 439-459 ◽  
Author(s):  
Helmut Eckelmann
Keyword(s):  
Channel Flow ◽  
Turbulent Channel Flow ◽  
Streamwise Velocity ◽  
Viscous Sublayer ◽  
Wall Region ◽  
Normal Velocity ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
Mean Values ◽  
The Mean

Hot-film anemometer measurements have been carried out in a fully developed turbulent channel flow. An oil channel with a thick viscous sublayer was used, which permitted measurements very close to the wall. In the viscous sublayer between y+ ≃ 0·1 and y+ = 5, the streamwise velocity fluctuations decreased at a higher rate than the mean velocity; in the region y+ [lsim ] 0·1, these fluctuations vanished at the same rate as the mean velocity.The streamwise velocity fluctuations u observed in the viscous sublayer and the fluctuations (∂u/∂y)0 of the gradient at the wall were almost identical in form, but the fluctuations of the gradient at the wall were found to lag behind the velocity fluctuations with a lag time proportional to the distance from the wall. Probability density distributions of the streamwise velocity fluctuations were measured. Furthermore, measurements of the skewness and flatness factors made by Kreplin (1973) in the same flow channel are discussed. Measurements of the normal velocity fluctuations v at the wall and of the instantaneous Reynolds stress −ρuv were also made. Periods of quiescence in the − ρuv signal were observed in the viscous sublayer as well as very active periods where ratios of peak to mean values as high as 30:1 occurred.

scholarly journals The quiescent core of turbulent channel flow

2014 ◽  
Vol 751 ◽  
pp. 228-254 ◽  
Author(s):  
Y. S. Kwon ◽  
J. Philip ◽  
C. M. de Silva ◽  
N. Hutchins ◽  
J. P. Monty
Keyword(s):  
Channel Flow ◽  
Large Scale ◽  
Turbulent Channel Flow ◽  
Streamwise Velocity ◽  
Core Region ◽  
Wall Turbulence ◽  
The Core ◽  
Velocity Magnitude ◽  
Core Boundary ◽  
Centreline Velocity

AbstractThe identification of uniform momentum zones in wall-turbulence, introduced by Adrian, Meinhart & Tomkins (J. Fluid Mech., vol. 422, 2000, pp. 1–54) has been applied to turbulent channel flow, revealing a large ‘core’ region having high and uniform velocity magnitude. Examination of the core reveals that it is a region of relatively weak turbulence levels. For channel flow in the range $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}Re_{\tau } = 1000\text {--}4000$, it was found that the ‘core’ is identifiable by regions bounded by the continuous isocontour lines of the streamwise velocity at $0.95U_{CL}$ (95 % of the centreline velocity). A detailed investigation into the properties of the core has revealed it has a large-scale oscillation which is predominantly anti-symmetric with respect to the channel centreline as it moves through the channel, and there is a distinct jump in turbulence statistics as the core boundary is crossed. It is concluded that the edge of the core demarcates a shear layer of relatively intense vorticity such that the interior of the core contains weakly varying, very low-level turbulence (relative to the flow closer to the wall). Although channel flows are generally referred to as ‘fully turbulent’, these findings suggest there exists a relatively large and ‘quiescent’ core region with a boundary qualitatively similar to the turbulent/non-turbulent interface of boundary layers, jets and wakes.

scholarly journals Correlation between small-scale velocity and scalar fluctuations in a turbulent channel flow

2009 ◽  
Vol 627 ◽  
pp. 1-32 ◽  
Author(s):  
HIROYUKI ABE ◽  
ROBERT ANTHONY ANTONIA ◽  
HIROSHI KAWAMURA
Keyword(s):  
Strain Rate ◽  
Channel Flow ◽  
Dissipation Rate ◽  
Compressive Strain ◽  
Outer Region ◽  
Turbulent Channel Flow ◽  
Scalar Fields ◽  
Scalar Dissipation ◽  
Small Scale ◽  
Scalar Dissipation Rate

Direct numerical simulations of a turbulent channel flow with passive scalar transport are used to examine the relationship between small-scale velocity and scalar fields. The Reynolds number based on the friction velocity and the channel half-width is equal to 180, 395 and 640, and the molecular Prandtl number is 0.71. The focus is on the interrelationship between the components of the vorticity vector and those of the scalar derivative vector. Near the wall, there is close similarity between different components of the two vectors due to the almost perfect correspondence between the momentum and thermal streaks. With increasing distance from the wall, the magnitudes of the correlations become smaller but remain non-negligible everywhere in the channel owing to the presence of internal shear and scalar layers in the inner region and the backs of the large-scale motions in the outer region. The topology of the scalar dissipation rate, which is important for small-scale scalar mixing, is shown to be associated with the organized structures. The most preferential orientation of the scalar dissipation rate is the direction of the mean strain rate near the wall and that of the fluctuating compressive strain rate in the outer region. The latter region has many characteristics in common with several turbulent flows; viz. the dominant structures are sheetlike in form and better correlated with the energy dissipation rate than the enstrophy.

Topology of fine-scale motions in turbulent channel flow

1996 ◽  
Vol 310 ◽  
pp. 269-292 ◽  
Author(s):  
Hugh M. Blackburn ◽  
Nagi N. Mansour ◽  
Brian J. Cantwell
Keyword(s):  
Strain Rate ◽  
Channel Flow ◽  
Velocity Gradient ◽  
Outer Region ◽  
Turbulent Channel Flow ◽  
Principal Strain ◽  
Wall Region ◽  
Fine Scale ◽  
Stable Focus ◽  
Topological Features

An investigation of topological features of the velocity gradient field of turbulent channel flow has been carried out using results from a direct numerical simulation for which the Reynolds number based on the channel half-width and the centreline velocity was 7860. Plots of the joint probability density functions of the invariants of the rate of strain and velocity gradient tensors indicated that away from the wall region, the fine-scale motions in the flow have many characteristics in common with a variety of other turbulent and transitional flows: the intermediate principal strain rate tended to be positive at sites of high viscous dissipation of kinetic energy, while the invariants of the velocity gradient tensor showed that a preference existed for stable focus/stretching and unstable node/saddle/saddle topologies. Visualization of regions in the flow with stable focus/stretching topologies revealed arrays of discrete downstream-leaning flow structures which originated near the wall and penetrated into the outer region of the flow. In all regions of the flow, there was a strong preference for the vorticity to be aligned with the intermediate principal strain rate direction, with the effect increasing near the walls in response to boundary conditions.

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