Scaling of the streamwise turbulence intensity in the context of inner-outer interactions in wall turbulence *
17 Oct 2017-Vol. 2, Iss: 10, pp 100502
TL;DR: In this paper, an established model for such an interaction between near-wall and logarithmic region turbulence is considered that comprises two mechanisms: superposition and modulation, where outer-region motions, of which a fraction is wall-attached, are superimposed onto the near wall dynamics, and concurrently the nearwall motions are modulated by this superimposed signature.
Abstract: The classical view of wall-bounded turbulence considers a near-wall inner region where all velocity statistics are universally dependent on distance from the wall when scaled with friction velocity and the kinematic viscosity of the fluid. This is referred to as an inner scaling and leads to Prandtl's law of the wall. Data from numerical simulations and experiments over the past decade or so, however, have provided compelling evidence that statistics of the fluctuating streamwise velocity do not follow inner scaling in this near-wall region and an interaction of outer and logarithmic regions exists, resulting in a Reynolds number dependence. In this paper we briefly review some of these studies and discuss the Reynolds number dependence of the streamwise turbulence intensity near the wall in terms of an inner-outer interaction. An established model for such an interaction between near-wall and logarithmic region turbulence is considered that comprises two mechanisms: superposition and modulation. Here outer-region motions, of which a fraction is wall-attached, are superimposed onto the near-wall dynamics, and concurrently the near-wall motions are modulated by this superimposed signature. We discuss to what extent the superposition effect can relate changes in the inner-scaled near-wall peak value of streamwise turbulence intensity to logarithmic region turbulence resembling features of attached eddies.
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TL;DR: In this paper, the authors used the nano-scale thermal anemometry probe (NSTAP), developed at Princeton University to conduct velocity measurements in the high Reynolds number boundary layer facility at the University of Melbourne.
Abstract: Fully resolved measurements of turbulent boundary layers are reported for the Reynolds number range . Despite several decades of research in wall-bounded turbulence there is still controversy over the behaviour of streamwise turbulence intensities near the wall, especially at high Reynolds numbers. Much of it stems from the uncertainty in measurement due to finite spatial resolution. Conventional hot-wire anemometry is limited for high Reynolds number measurements due to limited spatial resolution issues that cause attenuation in the streamwise turbulence intensity profile near the wall. To address this issue we use the nano-scale thermal anemometry probe (NSTAP), developed at Princeton University to conduct velocity measurements in the high Reynolds number boundary layer facility at the University of Melbourne. The NSTAP has a sensing length almost one order of magnitude smaller than conventional hot-wires. This enables us to acquire fully resolved velocity measurements of turbulent boundary layers up to . Results show that in the near-wall region, the viscous-scaled streamwise turbulence intensity grows with in the Reynolds number range of the experiments. A second outer peak in the streamwise turbulence intensity is also shown to emerge at the highest Reynolds numbers. Moreover, the energy spectra in the near-wall region show excellent inner scaling over the small to moderate wavelength range, followed by a large-scale influence that increases with Reynolds number. Outer scaling in the outer region is found to collapse the energy spectra over high wavelengths across various Reynolds numbers.
96 citations
TL;DR: In this article, the authors demonstrate the logarithmic region of the turbulence intensity by identifying wall-attached structures of the velocity fluctuations ( structures) and suggest that these structures are prime candidates for Townsend's attached-eddy hypothesis and that they can serve as cornerstones for understanding the multiscale phenomena of high-Reynolds-number boundary layers.
Abstract: Wall turbulence is a ubiquitous phenomenon in nature and engineering applications, yet predicting such turbulence is difficult due to its complexity. High-Reynolds-number turbulence arises in most practical flows, and is particularly complicated because of its wide range of scales. Although the attached-eddy hypothesis postulated by Townsend can be used to predict turbulence intensities and serves as a unified theory for the asymptotic behaviours of turbulence, the presence of coherent structures that contribute to the logarithmic behaviours has not been observed in instantaneous flow fields. Here, we demonstrate the logarithmic region of the turbulence intensity by identifying wall-attached structures of the velocity fluctuations ( structures. These findings suggest that the identified structures are prime candidates for Townsend’s attached-eddy hypothesis and that they can serve as cornerstones for understanding the multiscale phenomena of high-Reynolds-number boundary layers.
94 citations
01 Nov 2016
TL;DR: In this article, the authors review wall-bounded turbulent flows, particularly high-Reynolds number, zero-pressure gradient boundary layers, and fully developed pipe and channel flows.
Abstract: We review wall-bounded turbulent flows, particularly high–Reynolds number, zero–pressure gradient boundary layers, and fully developed pipe and channel flows. It is apparent that the approach to an asymptotically high–Reynolds number state is slow, but at a sufficiently high Reynolds number the log law remains a fundamental part of the mean flow description. With regard to the coherent motions, very-large-scale motions or superstructures exist at all Reynolds numbers, but they become increasingly important with Reynolds number in terms of their energy content and their interaction with the smaller scales near the wall. There is accumulating evidence that certain features are flow specific, such as the constants in the log law and the behavior of the very large scales and their interaction with the large scales (consisting of vortex packets). Moreover, the refined attached-eddy hypothesis continues to provide an important theoretical framework for the structure of wall-bounded turbulent flows.
61 citations
TL;DR: In this article, the authors proposed a new wall-scaling algorithm for turbulent flows near smooth walls, where the streamwise velocity fluctuation is bounded by a boundedness on the dissipation rate at the wall.
Abstract: The celebrated wall-scaling works for many statistical averages in turbulent flows near smooth walls, but the streamwise velocity fluctuation, owing to the natural constraint of boundedness on the dissipation rate at the wall. This new formula agrees well with the existing data and, in contrast to the logarithmic growth, supports the classical wall-scaling for turbulent intensity at asymptotically high Reynolds numbers.
59 citations
Cites background or methods from "Scaling of the streamwise turbulenc..."
...Also, data of Vincenti et al. (2013) are not taken from any plot in Marusic et al. (2017) but from original data authors....
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...The reason for this logarithmic growth, according to Marusic et al. (2017), is the inner–outer interaction between near wall and outer flow eddies, 908 R3-2 captured in good measure by the attached-eddy model of Townsend....
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...With the two fitting parameters A = 0.63 and B = 3.80 given in Marusic et al. (2017), (1.1) represents the data quite well, as the solid line in figure 1 shows....
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...Note that differing from Marusic et al. (2017) where Re of TBL was defined by the thickness obtained via mean velocity log-law fitting (see Marusic et al. (2015) for details), we use δ99 as the boundary layer thickness and hence Re = uτ δ99/ν for TBL flows....
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TL;DR: In this paper, the spectral proper orthogonal decomposition (SPOD) was used to identify energetically dominant coherent structures, most of which turn out to be streaks and quasi-streamwise vortices.
Abstract: Direct numerical simulations, performed with a high-order spectral-element method, are used to study coherent structures in turbulent pipe flow at friction Reynolds numbers . The database was analysed using spectral proper orthogonal decomposition (SPOD) to identify energetically dominant coherent structures, most of which turn out to be streaks and quasi-streamwise vortices. To understand how such structures can be modelled, the linear flow responses to harmonic forcing were computed using the singular value decomposition of the resolvent operator, using the mean field as a base flow. The SPOD and resolvent analysis were calculated for several combinations of frequencies and wavenumbers, allowing the mapping out of similarities between SPOD modes and optimal responses for a wide range of relevant scales in turbulent pipe flows. In order to explore physical reasons behind the agreement between both methods, an indicator of lift-up mechanism in the resolvent analysis was introduced, activated when optimal forcing is dominated by the wall-normal and azimuthal components, and associated response corresponds to streaks of streamwise velocity. Good agreement between leading SPOD and resolvent modes is observed in a large region of parameter space. In this region, a significant gain separation is found in resolvent analysis, which may be attributed to the strong amplification associated with the lift-up mechanism, here understood as nonlinear forcing terms leading to the appearance of streamwise vortices, which in turn form high-amplitude streaks. For both Reynolds numbers, the observed concordances were generally for structures with large energy in the buffer layer. The results highlight resolvent analysis as a pertinent reduced-order model for coherent structures in wall-bounded turbulence, particularly for streamwise elongated structures corresponding to near-wall streamwise vortices and streaks.
57 citations
References
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TL;DR: In this paper, the structure of energy-containing turbulence in the outer region of a zero-pressure-gradient boundary layer has been studied using particle image velocimetry (PIV) to measure the instantaneous velocity fields in a streamwise-wall-normal plane.
Abstract: The structure of energy-containing turbulence in the outer region of a zero-pressure-
gradient boundary layer has been studied using particle image velocimetry (PIV) to measure the instantaneous velocity fields in a streamwise-wall-normal plane. Experiments performed at three Reynolds numbers in the range 930 0) that occur on a locus inclined at 30–60° to the wall.In the outer layer, hairpin vortices occur in streamwise-aligned packets that propagate with small velocity dispersion. Packets that begin in or slightly above the buffer layer are very similar to the packets created by the autogeneration mechanism (Zhou, Adrian & Balachandar 1996). Individual packets grow upwards in the streamwise direction at a mean angle of approximately 12°, and the hairpins in packets are typically spaced several hundred viscous lengthscales apart in the streamwise direction. Within the interior of the envelope the spatial coherence between the velocity fields induced by the individual vortices leads to strongly retarded streamwise momentum, explaining the zones of uniform momentum observed by Meinhart & Adrian (1995). The packets are an important type of organized structure in the wall layer in which relatively small structural units in the form of three-dimensional vortical structures are arranged coherently, i.e. with correlated spatial relationships, to form much longer structures. The formation of packets explains the occurrence of multiple VITA events in turbulent ‘bursts’, and the creation of Townsend's (1958) large-scale inactive motions. These packets share many features of the hairpin models proposed by Smith (1984) and co-workers for the near-wall layer, and by Bandyopadhyay (1980), but they are shown to occur in a hierarchy of scales across most of the boundary layer.In the logarithmic layer, the coherent vortex packets that originate close to the wall frequently occur within larger, faster moving zones of uniform momentum, which may extend up to the middle of the boundary layer. These larger zones are the induced interior flow of older packets of coherent hairpin vortices that originate upstream and over-run the younger, more recently generated packets. The occurence of small hairpin packets in the environment of larger hairpin packets is a prominent feature of the logarithmic layer. With increasing Reynolds number, the number of hairpins in a packet increases.
1,627 citations
"Scaling of the streamwise turbulenc..." refers background in this paper
...The attached eddy framework, as originally put forward by Townsend, was an attempt to explain time-averaged statistics; however, recent papers [41,42] have demonstrated that a distribution of representative eddies can produce instantaneous features that qualitatively match observed instantaneous behavior in turbulent boundary layers regarding uniform momentum zones [43] and internal shear layers [44,45]....
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...Again, this coherence reflects a self-similar structure of wall-attached turbulence and the existence of wall-coherent larger-scale motions [43]....
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TL;DR: In this article, a publisher's version of an article published in Journal of Fluid Mechanics © 2007 Cambridge University Press, Cambridge, UK. www.cambridge.edu.org/
Abstract: This is a publisher’s version of an article published in Journal of Fluid Mechanics © 2007 Cambridge University Press. www.cambridge.org/
1,197 citations
"Scaling of the streamwise turbulenc..." refers background in this paper
...This organization is often described via a classification of coherent structures [52], including hairpin vortices, large-scale motions, and very-large-scale motions (or superstructures [3])....
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TL;DR: In this article, a new numerical simulation of a turbulent channel in a large box at Reτ=2003 is described and briefly compared with simulations at lower Reynolds numbers and with experiments.
Abstract: A new numerical simulation of a turbulent channel in a large box at Reτ=2003 is described and briefly compared with simulations at lower Reynolds numbers and with experiments. Some of the fluctuation intensities, especially the streamwise velocity, do not scale well in wall units, both near and away from the wall. Spectral analysis traces the near-wall scaling failure to the interaction of the logarithmic layer with the wall. The present statistics can be downloaded from http://torroja.dmt.upm.es/ftp/channels. Further ones will be added to the site as they become available.
1,018 citations
"Scaling of the streamwise turbulenc..." refers background or methods in this paper
...DNS channel data of Lee and Moser [17] are considered, as well as the DNS channel data of Hoyas and Jiménez [16], which matches the TBL DNS data point of Sillero et al....
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...DNS data of (LM15) Lee and Moser [17] at Reτ ≈ 550, 1000, and 5200 (channel), (HJ06) Hoyas and Jiménez [16] at Reτ ≈ 2000 (channel), and (SJM13) Sillero, Jiménez, and Moser [56] at Reτ ≈ 2000 (TBL)....
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...DNS channel data of Lee and Moser [17] are considered, as well as the DNS channel data of Hoyas and Jiménez [16], which matches the TBL DNS data point of Sillero et al. [56]....
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...In a trail of observations it was identified that a scale interaction exists between the larger (coherent) scales and the smaller (incoherent) scales [4,16,19,29,71]....
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...63 has also been observed for DNS data [16,17,56] and describes boundary layer data taken at the Flow Physics Facility [81]....
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TL;DR: In this article, it is shown that a cycle exists which is local to the near-wall region and does not depend on the outer flow, and that the presence of the wall seems to be only necessary to maintain the mean shear.
Abstract: Numerical experiments on modified turbulent channels at moderate Reynolds numbers are used to differentiate between several possible regeneration cycles for the turbulent fluctuations in wall-bounded flows. It is shown that a cycle exists which is local to the near-wall region and does not depend on the outer flow. It involves the formation of velocity streaks from the advection of the mean profile by streamwise vortices, and the generation of the vortices from the instability of the streaks. Interrupting any of those processes leads to laminarization. The presence of the wall seems to be only necessary to maintain the mean shear. The generation of secondary vorticity at the wall is shown to be of little importance in turbulence generation under natural circumstances. Inhibiting its production increases turbulence intensity and drag.
867 citations
"Scaling of the streamwise turbulenc..." refers background or result in this paper
...The pioneering work in minimal channels by Jiménez and Pinelli [25] cemented the view that this cycle is “autonomous”; it does not require external triggers from outer larger-scale eddies to self-sustain....
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...[25] J. Jiménez and A. Pinelli, The autonomous cycle of near-wall turbulence, J. Fluid Mech....
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...In both cases the self-similar “representative” eddy seemed reminiscent of the self-sustaining process observed for the near-wall cycle by Jiménez and Pinelli [25] and Schoppa and Hussain [35]....
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TL;DR: A review of organized motion in turbulent flow indicates that the transport properties of most shear flows are dominated by large-scale vortex nonrandom motions as mentioned in this paper, and the boundary layer coherent structure was isolated by the correlation methods of Townsend (1956) and flow visualization by direct observations of complex unsteady turbulent motions.
Abstract: A review of organized motion in turbulent flow indicates that the transport properties of most shear flows are dominated by large-scale vortex nonrandom motions. The mean velocity profile of a turbulent boundary layer consists of a viscous sublayer, buffer layer, and a logarithmic outer layer; an empirical formula of Coles (1956) applies to various pressure gradients. The boundary layer coherent structure was isolated by the correlation methods of Townsend (1956) and flow visualization by direct observations of complex unsteady turbulent motions. The near-wall studies of Willmart and Wooldridge (1962) used the space-time correlation for pressure fluctuations at the wall under a thick turbulent boundary layer; finally, organized motion in free shear flows and transition-control of mixing demonstrated that the Reynolds number invariance of turbulence shows wide scatter.
826 citations
"Scaling of the streamwise turbulenc..." refers background in this paper
...On the coherence along the wall-normal direction An organization in high-Reynolds-number wall turbulence is most pronounced in the logarithmic region where large-scale turbulent structures comprise significant lifetimes in the streamwise direction [24,55]....
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