The quiescent core of turbulent channel flow

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.

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

Journal of Fluid Mechanics ◽

10.1017/jfm.2018.434 ◽

2018 ◽

Vol 850 ◽

pp. 733-768 ◽

Cited By ~ 12

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).

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

Journal of Fluid Mechanics ◽

10.1017/jfm.2014.249 ◽

2014 ◽

Vol 749 ◽

pp. 818-840 ◽

Cited By ~ 39

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.

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

Journal of Fluid Mechanics ◽

10.1017/jfm.2017.526 ◽

2017 ◽

Vol 828 ◽

pp. 424-458 ◽

Cited By ~ 18

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 $Re$.

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Invariant solutions of minimal large-scale structures in turbulent channel flow for up to 1000

Journal of Fluid Mechanics ◽

10.1017/jfm.2016.470 ◽

2016 ◽

Vol 802 ◽

Cited By ~ 26

Author(s):

Yongyun Hwang ◽

Ashley P. Willis ◽

Carlo Cossu

Keyword(s):

Channel Flow ◽

Large Scale ◽

Turbulent Channel Flow ◽

The Self ◽

Wall Turbulence ◽

Small Scale ◽

Invariant Solutions ◽

Large Scale Structures ◽

Turbulent Statistics ◽

Scale Structures

Understanding the origin of large-scale structures in high-Reynolds-number wall turbulence has been a central issue over a number of years. Recently, Rawat et al. (J. Fluid Mech., vol. 782, 2015, pp. 515–540) have computed invariant solutions for the large-scale structures in turbulent Couette flow at $Re_{\unicode[STIX]{x1D70F}}\simeq 128$ using an overdamped large-eddy simulation with the Smagorinsky model to account for the effect of the surrounding small-scale motions. Here, we extend this approach to Reynolds numbers an order of magnitude higher in turbulent channel flow, towards the regime where the large-scale structures in the form of very-large-scale motions (long streaky motions) and large-scale motions (short vortical structures) emerge energetically. We demonstrate that a set of invariant solutions can be computed from simulations of the self-sustaining large-scale structures in the minimal unit (domain of size $L_{x}=3.0h$ streamwise and $L_{z}=1.5h$ spanwise) with midplane reflection symmetry at least up to $Re_{\unicode[STIX]{x1D70F}}\simeq 1000$. By approximating the surrounding small scales with an artificially elevated Smagorinsky constant, a set of equilibrium states are found, labelled upper- and lower-branch according to their associated drag. It is shown that the upper-branch equilibrium state is a reasonable proxy for the spatial structure and the turbulent statistics of the self-sustaining large-scale structures.

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

Journal of Fluid Mechanics ◽

10.1017/jfm.2016.3 ◽

2016 ◽

Vol 790 ◽

pp. 128-157 ◽

Cited By ~ 39

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.

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Direct numerical simulation of turbulent channel flow up to

Journal of Fluid Mechanics ◽

10.1017/jfm.2015.268 ◽

2015 ◽

Vol 774 ◽

pp. 395-415 ◽

Cited By ~ 420

Author(s):

Myoungkyu Lee ◽

Robert D. Moser

Keyword(s):

Numerical Simulation ◽

Reynolds Number ◽

Direct Numerical Simulation ◽

Turbulent Flows ◽

Channel Flow ◽

Turbulent Channel Flow ◽

Streamwise Velocity ◽

Mean Velocity ◽

Layer Structures ◽

High Reynolds

A direct numerical simulation of incompressible channel flow at a friction Reynolds number ($\mathit{Re}_{{\it\tau}}$) of 5186 has been performed, and the flow exhibits a number of the characteristics of high-Reynolds-number wall-bounded turbulent flows. For example, a region where the mean velocity has a logarithmic variation is observed, with von Kármán constant ${\it\kappa}=0.384\pm 0.004$. There is also a logarithmic dependence of the variance of the spanwise velocity component, though not the streamwise component. A distinct separation of scales exists between the large outer-layer structures and small inner-layer structures. At intermediate distances from the wall, the one-dimensional spectrum of the streamwise velocity fluctuation in both the streamwise and spanwise directions exhibits $k^{-1}$ dependence over a short range in wavenumber $(k)$. Further, consistent with previous experimental observations, when these spectra are multiplied by $k$ (premultiplied spectra), they have a bimodal structure with local peaks located at wavenumbers on either side of the $k^{-1}$ range.

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Large-Scale Forcing of a Turbulent Channel Flow Through Spanwise Synthetic Jets

AIAA Journal ◽

10.2514/1.j059047 ◽

2020 ◽

Vol 58 (5) ◽

pp. 2042-2052 ◽

Cited By ~ 2

Author(s):

M. Cannata ◽

G. Cafiero ◽

G. Iuso

Keyword(s):

Channel Flow ◽

Large Scale ◽

Turbulent Channel Flow ◽

Synthetic Jets ◽

Flow Through

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Coherent structures in the linearized impulse response of turbulent channel flow

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.15 ◽

2019 ◽

Vol 863 ◽

pp. 1190-1203 ◽

Cited By ~ 9

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.

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