31325200
Pressure gradient effects on the large-scale structure of turbulent boundary layers
Abstract Research into high-Reynolds-number turbulent boundary layers in recent years has brought about a renewed interest in the larger-scale structures. It is now known that these structures emerge more prominently in the outer region not only due to increased Reynolds number (Metzger & Klewicki, Phys. Fluids, vol. 13(3), 2001, pp. 692–701; Hutchins & Marusic, J. Fluid Mech., vol. 579, 2007, pp. 1–28), but also when a boundary layer is exposed to an adverse pressure gradient (Bradshaw, J. Fluid Mech., vol. 29, 1967, pp. 625–645; Lee & Sung, J. Fluid Mech., vol. 639, 2009, pp. 101–131). The latter case has not received as much attention in the literature. As such, this work investigates the modification of the large-scale features of boundary layers subjected to zero, adverse and favourable pressure gradients. It is first shown that the mean velocities, turbulence intensities and turbulence production are significantly different in the outer region across the three cases. Spectral and scale decomposition analyses confirm that the large scales are more energized throughout the entire adverse pressure gradient boundary layer, especially in the outer region. Although more energetic, there is a similar spectral distribution of energy in the wake region, implying the geometrical structure of the outer layer remains universal in all cases. Comparisons are also made of the amplitude modulation of small scales by the large-scale motions for the three pressure gradient cases. The wall-normal location of the zero-crossing of small-scale amplitude modulation is found to increase with increasing pressure gradient, yet this location continues to coincide with the large-scale energetic peak wall-normal location (as has been observed in zero pressure gradient boundary layers). The amplitude modulation effect is found to increase as pressure gradient is increased from favourable to adverse.
120617142
Very large-scale motion in the outer layer
Very large-scale motions in the form of long regions of streamwise velocity fluctuation are observed in the outer layer of fully developed turbulent pipe flow over a range of Reynolds numbers. The premultiplied, one-dimensional spectrum of the streamwise velocity measured by hot-film anemometry has a bimodal distribution whose components are associated with large-scale motion and a range of smaller scales corresponding to the main turbulent motion. The characteristic wavelength of the large-scale mode increases through the logarithmic layer, and reaches a maximum value that is approximately 12–14 times the pipe radius, one order of magnitude longer than the largest reported integral length scale, and more than four to five times longer than the length of a turbulent bulge. The wavelength decreases to approximately two pipe radii at the pipe centerline. It is conjectured that the very large-scale motions result from the coherent alignment of large-scale motions in the form of turbulent bulges or packets of...
122734856
The turbulence structure of equilibrium boundary layers
Measurements in three boundary layers, one with constant free-stream velocity and two with power-law variations of free-stream velocity giving ‘moderate’ and ‘strong’ adverse pressure gradients, are presented and discussed. Several unifying features of the turbulent motion, expected to appear in all boundary layers not too far from equilibrium, are identified. The intensity spectra at higher wavenumbers follow the Kolmogorov inertial-subrange law, although the Reynolds number is not particularly high even by laboratory standards: in addition the smaller-scale motion in the outer layer is determined entirely by the local shear stress and the boundary-layer thickness. The large eddy motion increases in strength relative to the general turbulence level as the general turbulence level increases, and the limited evidence available suggests that the large eddies are similar to those in the free mixing layer. In all cases the large eddies contribute a significant proportion of the shear stress in the outer layer.
122828226
AN EXPERIMENTAL INVESTIGATION OF AN INCOMPRESSIBLE TURBULENT BOUNDARY LAYER IN THE VICINITY OF SEPARATION
The paper is about an investigation into the effects of small changes in the static pressure distribution on the development of an axisymmetric, incompressible, turbulent boundary layer with incipient separation. The pressure distribution was closely controlled to study three cases, in which the skin friction was either approximately zero, slightly negative or slightly positive along a fixed length. Mean flow and turbulence structure in air were measured using pulsed-wire and hot-wire anemometry.
123987742
A turbulent equilibrium boundary layer near separation
The experimental results for an equilibrium boundary layer in a strong adverse pressure gradient flow are reported. The measurements show that similarity in the mean flow and the turbulent stresses has been achieved over a substantial streamwise distance where the skin friction coefficient is kept at a low, constant level. Although the Reynolds stress distribution across the layer is entirely different from the flow at zero pressure gradient, the ratios between the different turbulent stress components were found to be similar, showing that the mechanism for distributing the turbulent energy between the different components remains unaffected by the mean flow pressure gradient. Close to the surface the gradient of the mixing length was found to increase from K l ≈ 0.41 to K l ≈ 0.78, almost twice as high as for the zero pressure gradient case. Similarity in the triple correlations was also found to be good. The correlations show that there is a considerable diffusion of turbulent energy from the central part of the boundary layer towards the wall. The diffusion mechanism is caused by a second peak in the turbulence production, located at y /δ ≈ 0.45. This production was for the present case almost as strong as the production found near the wall. The energy budget for the turbulent kinetic energy also shows that strong dissipation is not restricted to the wall region, but is significant for most of the layer.
121233904
EQUILIBRIUM LAYERS AND WALL TURBULENCE
In turbulent flow past rigid boundaries, there can be distinguished regions close to the wall in which the local rates of energy production and dissipation are so large that aspects of the turbulent motion concerned with these processes are determined almost solely by the distribution of shear stress within the region and are independent of conditions outside it. These regions are called equilibrium layers because of the equilibrium existing between local rates of energy production and dissipation. The properties of these various equilibrium layers are considered and the distributions of mean velocity are derived from the equation for the turbulent kinetic energy and certain assumptions of flow similarity. The theory of self-preserving wall flow, usually expressed as a combination of the law of the wall and defect law, assumes compatibility between the outer flow and the equilibrium layer, and the course of development depends on the kind of equilibrium layer. Ear the whole of the equilibrium layer is a constant-stress layer and this is not true in strong adverse pressure gradients. A consistent theory is developed for these flows by assuming a linear-stress layer, and the solutions show the relation between flows of finite stress and of zero stress andmore » provide a plausible explanation of the phenomenon of downstream instability observed by Clauser. Selfpreserving flow in wedges is treated on similar lines. (auth)« less
119480444
‘Inactive’ motion and pressure fluctuations in turbulent boundary layers
Townsend's (1961) hypothesis that the turbulent motion in the inner region of a boundary layer consists of (i) an ‘active’ part which produces the shear stress τ and whose statistical properties are universal functions of τ and y , and (ii) an ‘inactive’ and effectively irrotational part determined by the turbulence in the outer layer, is supported in the present paper by measurements of frequency spectra in a strongly retarded boundary layer, in which the ‘inactive’ motion is particularly intense. The only noticeable effect of the inactive motion is an increased dissipation of kinetic energy into heat in the viscous sublayer, supplied by turbulent energy diffusion from the outer layer towards the surface. The required diffusion is of the right order of magnitude to explain the non-universal values of the triple products measured near the surface, which can therefore be reconciled with universality of the ‘active’ motion. Dimensional analysis shows that the contribution of the ‘active’ inner layer motion to the one-dimensional wave-number spectrum of the surface pressure fluctuations varies as τ 2 w / k 1 up to a wave-number inversely proportional to the thickness of the viscous sublayer. This result is strongly supported by the recent measurements of Hodgson (1967), made with a much smaller ratio of microphone diameter to boundary-layer thickness than has been achieved previously. The disagreement of the result with most other measurements is attributed to inadequate transducer resolution in the other experiments.
115473275
Numerical study of a separation bubble with heat transfer
We present a Direct Numerical Simulation of the rapid separation and reattachment of the turbulent boundary layer on a flat wall. The temperature is a passive scalar, with an isothermal wall. Prescribed suction and blowing along an inviscid boundary opposite the layer create the required pressure gradients. The transpiration profile is defined analytically, inflow profiles are given, and outflow conditions are non-critical; this allows duplication of the flow. The incoming boundary layer is turbulent, but unfortunately not perfectly developed, primarily due to Reynolds-number constraints. These constraints come from the high computing cost and are also the reason for making the bubble unusually short. The mean quantities and Reynolds stresses reveal that the severe distortion of the turbulent layer associated with separation defeats not only the boundary-layer assumptions, but also several assumptions convenient in turbulence modelling; negative production of turbulent kinetic energy and counter-gradient heat transfer are observed locally. The Reynolds analogy between velocity and temperature fields weakens to the extent that the wall heat transfer increases just where the momentum transfer collapses.
122742285
Direct numerical simulation of a separated turbulent boundary layer
A separated turbulent boundary layer over a flat plate was investigated by direct numerical simulation of the incompressible Navier-Stokes equations. A suction-blowing velocity distribution was prescribed along the upper boundary of the computational domain to create an adverse-to-favourable pressure gradient that produces a closed separation bubble. The Reynolds number based on inlet free-stream velocity and momentum thickness is 300. Neither instantaneous detachment nor reattachment points are fixed in space but fluctuate significantly. The mean detachment and reattachment locations determined by three different definitions, i.e. (i) location of 50% forward flow fraction, (ii) mean dividing streamline (ψ = 0), (iii) location of zero wall-shear stress (τ w = 0), are in good agreement. Instantaneous vorticity contours show that the turbulent structures emanating upstream of separation move upwards into the shear layer in the detachment region and then turn around the bubble. The locations of the maximum turbulence intensities as well as Reynolds shear stress occur in the middle of the shear layer
122656995
Structures in turbulent boundary layers subjected to adverse pressure gradients
The effects of adverse pressure gradients on turbulent structures were investigated by carrying out direct numerical simulations of turbulent boundary layers subjected to adverse and zero pressure gradients. The equilibrium adverse pressure gradient flows were established by using a power law free-stream distribution U∞ ~ xm. Two-point correlations of velocity fluctuations were used to show that the spanwise spacing between near-wall streaks is affected significantly by a strong adverse pressure gradient. Low-momentum regions are dominant in the middle of the boundary layer as well as in the log layer. Linear stochastic estimation was used to provide evidence for the presence of low-momentum regions and to determine their statistical properties. The mean width of such large-scale structures is closely associated with the size of the hairpin-like vortices in the outer layer. The conditionally averaged flow fields around events producing Reynolds stress show that hairpin-like vortices are the structures associated with the production of outer turbulence. The shapes of the vortices beyond the log layer were found to be similar when their length scales were normalized according to the boundary layer thickness. Estimates of the conditionally averaged velocity fields associated with the spanwise vortical motion were obtained by using linear stochastic estimation. These results confirm that the outer region of the adverse pressure gradient boundary layer is populated with streamwise-aligned vortex organizations, which are similar to those of the vortex packet model proposed by Adrian, Meinhart & Tomkins (J. Fluid Mech., vol. 422, 2000, pp. 1–54). The adverse pressure gradient augments the inclination angles of the packets and the mean streamwise spacing of the vortex heads in the packets.
120583104
Large-scale structures in turbulent and reverse-transitional sink flow boundary layers
Aspects of large-scale organized structures in sink flow turbulent and reverse-transitional boundary layers are studied experimentally using hot-wire anemometry. Each of the present sink flow boundary layers is in a state of ‘perfect equilibrium’ or ‘exact self-preservation’ in the sense of Townsend (The Structure of Turbulent Shear Flow, 1st and 2nd edns, 1956, 1976, Cambridge University Press) and Rotta (Progr. Aeronaut. Sci., vol. 2, 1962, pp. 1–220) and conforms to the notion of ‘pure wall-flow’ (Coles, J. Aerosp. Sci., vol. 24, 1957, pp. 495–506), at least for the turbulent cases. It is found that the characteristic inclination angle of the structure undergoes a systematic decrease with the increase in strength of the streamwise favourable pressure gradient. Detectable wall-normal extent of the structure is found to be typically half of the boundary layer thickness. Streamwise extent of the structure shows marked increase as the favourable pressure gradient is made progressively severe. Proposals for the typical eddy forms in sink flow turbulent and reverse-transitional flows are presented, and the possibility of structural self-organization (i.e. individual hairpin vortices forming streamwise coherent hairpin packets) in these flows is also discussed. It is further indicated that these structural ideas may be used to explain, from a structural viewpoint, the phenomenon of soft relaminarization or reverse transition of turbulent boundary layers when subjected to strong streamwise favourable pressure gradients. Taylor's ‘frozen turbulence’ hypothesis is experimentally shown to be valid for flows in the present study even though large streamwise accelerations are involved, the flow being even reverse transitional in some cases. Possible conditions, which are required to be satisfied for the safe use of Taylor's hypothesis in pressure-gradient-driven flows, are also outlined. Measured convection velocities are found to be fairly close to the local mean velocities (typically 90% or more) suggesting that the structure gets convected downstream almost along with the mean flow.
26640881
A parametric study of adverse pressure gradient turbulent boundary layers
There are many open questions regarding the behaviour of turbulent boundary layers subjected to pressure gradients and this is confounded by the large parameter space that may affect these flows. While there have been many valuable investigations conducted within this parameter space, there are still insufficient data to attempt to reduce this parameter space. Here, we consider a parametric study of adverse pressure gradient turbulent boundary layers where we restrict our attention to the pressure gradient parameter, β, the Reynolds number and the acceleration parameter, K. The statistics analyzed are limited to the streamwise fluctuating velocity. The data show that the mean velocity profile in strong pressure gradient boundary layers does not conform to the classical logarithmic law. Moreover, there appears to be no measurable logarithmic region in these cases. It is also found that the large-scale motions scaling with outer variables are energised by the pressure gradient. These increasingly strong large-scale motions are found to be the dominant contributor to the increase in turbulence intensity (scaled with friction velocity) with increasing pressure gradient across the boundary layer.
121183842
Low- and high-speed structures in the outer region of an adverse-pressure-gradient turbulent boundary layer
Large- and very large-scale structures in the form of elongated regions of low and high streamwise momentum have been studied in the outer region of a turbulent boundary layer subjected to a strong adverse pressure gradient. Large sets of streamwise–spanwise instantaneous velocity fields are acquired by particle image velocimetry at three wall-normal positions (0.2δ, 0.5δ, 0.8δ) at three different streamwise locations and at 0.1δ at the last streamwise location which allows us to study the wall-normal and streamwise variations of the structures. Subsequently, a pattern-recognition method and a classification scheme are employed in order to detect, classify and characterize the structures in an efficient and rigorous manner. Like in the case of zero-pressure-gradient turbulent boundary layers, long meandering streaky regions of low and high momentum are observed in the outer region of the present flow but they appear less frequently; especially in the lower part (at 0.1δ and 0.2δ) of the large-velocity-defect zone, i.e. near detachment. The dimensions of these large structures scale on boundary-layer thickness (δ) and are generally comparable to those previously reported for such structures in the overlap region of zero-pressure-gradient turbulent boundary layers. Interestingly, the adverse pressure gradient does not significantly affect the dimensions and arrangement of the large-scale structures in the upper part (at 0.5δ and 0.8δ) a segment of the outer region where the scaled Reynolds stresses also remain fairly self-similar.
123274290
Influence of a strong adverse pressure gradient on the turbulent structure in a boundary layer
A comparison between the turbulent structures found in a zero pressure gradient boundary layer and a boundary layer subjected to a strong adverse pressure gradient is presented. The pressure gradient reverses the direction of the dominant turbulent diffusion, resulting in considerable turbulent transport towards the wall. Two‐point space–time correlations and the invariants show that this reduces the anisotropy in the near wall region and indicate an important reflection of the turbulent motion from the wall back into the outer layer. This is verified by a quadrant analysis [Lu and Willmarth, J. Fluid Mech. 60, 481 (1973)] which demonstrates that the strong events near the wall are totally dominated by motions in the first and fourth quadrants.
3173687
Evidence of very long meandering features in the logarithmic region of turbulent boundary layers
A regime of very long meandering positive and negative streamwise velocity fluctuations, that we term ‘superstructures’, are found to exist in the log and lower wake regions of turbulent boundary layers. Measurements are made with a spanwise rake of 10 hot-wires in two separate facilities (spanning more than a decade of Reτ) and are compared with existing PIV and DNS results. In all cases, we note evidence of a large-scale stripiness in the streamwise velocity fluctuations. The length of these regions can commonly exceed 20δ. Similar length scales have been previously reported for pipes and DNS channel flows. It is suggested that the true length of these features is masked from single-point statistics (such as autocorrelations and spectra) by a spanwise meandering tendency. Support for this conjecture is offered through the study of a synthetic flow composed only of sinusoidally meandering elongated low- and high-speed regions. From detailed maps of one-dimensional spectra, it is found that the contribution to the streamwise turbulence intensities associated with the superstructures appears to be increasingly significant with Reynolds number, and scales with outer length variables (δ). Importantly, the superstructure maintains a presence or footprint in the near-wall region, seeming to modulate or influence the near-wall cycle. This input of low-wavenumber outer-scaled energy into the near-wall region is consistent with the rise in near-wall streamwise intensities, when scaled with inner variables, that has been noted to occur with increasing Reynolds number. In an attempt to investigate these structures at very high Reynolds numbers, we also report on recent large-scale sonic anemometer rake measurements, made in the neutrally stable atmospheric surface layer. Preliminary results indicate that the superstructure is present in the log region of this atmospheric flow at Reτ = 6.6×105, and has a size consistent with outer scaling.
18465262
A comparison of turbulent pipe, channel and boundary layer flows
The extent or existence of similarities between fully developed turbulent pipes and channels, and in zero-pressure-gradient turbulent boundary layers has come into question in recent years. This is in contrast to the traditionally accepted view that, upon appropriate normalization, all three flows can be regarded as the same in the near-wall region. In this paper, the authors aim to provide clarification of this issue through streamwise velocity measurements in these three flows with carefully matched Reynolds number and measurement resolution. Results show that mean statistics in the near-wall region collapse well. However, the premultiplied energy spectra of streamwise velocity fluctuations show marked structural differences that cannot be explained by scaling arguments. It is concluded that, while similarities exist at these Reynolds numbers, one should exercise caution when drawing comparisons between the three shear flows, even near the wall.
10645266
Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers
In this paper we investigate the relationship between the large- and small-scale energy-containing motions in wall turbulence. Recent studies in a high-Reynolds-number turbulent boundary layer (Hutchins & Marusic, Phil. Trans. R. Soc. Lond. A, vol. 365, 2007a, pp. 647–664) have revealed a possible influence of the large-scale boundary-layer motions on the small-scale near-wall cycle, akin to a pure amplitude modulation. In the present study we build upon these observations, using the Hilbert transformation applied to the spectrally filtered small-scale component of fluctuating velocity signals, in order to quantify the interaction. In addition to the large-scale log-region structures superimposing a footprint (or mean shift) on the near-wall fluctuations (Townsend, The Structure of Turbulent Shear Flow, 2nd edn., 1976, Cambridge University Press; Metzger & Klewicki, Phys. Fluids, vol. 13, 2001, pp. 692–701.), we find strong supporting evidence that the small-scale structures are subject to a high degree of amplitude modulation seemingly originating from the much larger scales that inhabit the log region. An analysis of the Reynolds number dependence reveals that the amplitude modulation effect becomes progressively stronger as the Reynolds number increases. This is demonstrated through three orders of magnitude in Reynolds number, from laboratory experiments at Reτ ~ 103–104 to atmospheric surface layer measurements at Reτ ~ 106.
37127550
A wall-wake model for the turbulence structure of boundary layers. Part 2. Further experimental support
©Cambridge University Press. Marusic, Ivan and Perry A.E. (1995) A wall-wake model for the turbulence structure of boundary layers. Part 2. Further experimental support. Journal of fluid mechanics, 298, 389-407. http://www.jfm.damtp.cam.ac.uk/
46285763
Evolution and structure of sink-flow turbulent boundary layers
An experimental and theoretical investigation of turbulent boundary layers developing in a sink-flow pressure gradient was undertaken. Three flow cases were studied, corresponding to different acceleration strengths. Mean-flow measurements were taken for all three cases, while Reynolds stresses and spectra measurements were made for two of the flow cases. In this study attention was focused on the evolution of the layers to an equilibrium turbulent state. All the layers were found to attain a state very close to precise equilibrium. This gave equilibrium sink flow data at higher Reynolds numbers than in previous experiments. The mean velocity profiles were found to collapse onto the conventional logarithmic law of the wall. However, for profiles measured with the Pitot tube, a slight ‘kick-up’ from the logarithmic law was observed near the buffer region, whereas the mean velocity profiles measured with a normal hot wire did not exhibit this deviation from the logarithmic law. As the layers approached equilibrium, the mean velocity profiles were found to approach the pure wall profile and for the highest level of acceleration Π was very close to zero, where Π is the Coles wake factor. This supports the proposition of Coles (1957), that the equilibrium sink flow corresponds to pure wall flow. Particular interest was also given to the evolutionary stages of the boundary layers, in order to test and further develop the closure hypothesis of Perry, Marusic & Li (1994). Improved quantitative agreement with the experimental results was found after slight modification of their original closure equation.
17366256
Hot-wire spatial resolution issues in wall-bounded turbulence
Careful reassessment of new and pre-existing data shows that recorded scatter in the hot-wire-measured near-wall peak in viscous-scaled streamwise turbulence intensity is due in large part to the simultaneous competing effects of the Reynolds number and viscous-scaled wire length l+. An empirical expression is given to account for these effects. These competing factors can explain much of the disparity in existing literature, in particular explaining how previous studies have incorrectly concluded that the inner-scaled near-wall peak is independent of the Reynolds number. We also investigate the appearance of the so-called outer peak in the broadband streamwise intensity, found by some researchers to occur within the log region of high-Reynolds-number boundary layers. We show that the ‘outer peak’ is consistent with the attenuation of small scales due to large l+. For turbulent boundary layers, in the absence of spatial resolution problems, there is no outer peak up to the Reynolds numbers investigated here (Reτ = 18830). Beyond these Reynolds numbers – and for internal geometries – the existence of such peaks remains open to debate. Fully mapped energy spectra, obtained with a range of l+, are used to demonstrate this phenomenon. We also establish the basis for a ‘maximum flow frequency’, a minimum time scale that the full experimental system must be capable of resolving, in order to ensure that the energetic scales are not attenuated. It is shown that where this criterion is not met (in this instance due to insufficient anemometer/probe response), an outer peak can be reproduced in the streamwise intensity even in the absence of spatial resolution problems. It is also shown that attenuation due to wire length can erode the region of the streamwise energy spectra in which we would normally expect to see kx−1 scaling. In doing so, we are able to rationalize much of the disparity in pre-existing literature over the kx−1 region of self-similarity. Not surprisingly, the attenuated spectra also indicate that Kolmogorov-scaled spectra are subject to substantial errors due to wire spatial resolution issues. These errors persist to wavelengths far beyond those which we might otherwise assume from simple isotropic assumptions of small-scale motions. The effects of hot-wire length-to-diameter ratio (l/d) are also briefly investigated. For the moderate wire Reynolds numbers investigated here, reducing l/d from 200 to 100 has a detrimental effect on measured turbulent fluctuations at a wide range of energetic scales, affecting both the broadband intensity and the energy spectra.
20967558
Empirical mode decomposition and Hilbert transforms for analysis of oil-film interferograms
Oil-film interferometry is rapidly becoming the preferred method for direct measurement of wall shear stress in studies of wall-bounded turbulent flows. Although being widely accepted as the most accurate technique, it does have inherent measurement uncertainties, one of which is associated with determining the fringe spacing. This is the focus of this paper. Conventional analysis methods involve a certain level of user input and thus some subjectivity. In this paper, we consider empirical mode decomposition (EMD) and the Hilbert transform as an alternative tool for analyzing oil-film interferograms. In contrast to the commonly used Fourier-based techniques, this new method is less subjective and, as it is based on the Hilbert transform, is superior for treating amplitude and frequency modulated data. This makes it particularly robust to wide differences in the quality of interferograms.
124316059
Structure of turbulent boundary layer subjected to adverse pressure gradient
Abstract A turbulent boundary layer subjected to a sustained adverse pressure gradient is experimentally investigated. Waveforms of fluctuating velocity components in the boundary layer, especially in the near-wall region, are remarkably elongated in time in comparison with those in zero-pressure-gradient flows, and thus time scales increase with an increasing pressure gradient parameter $P^+$. The increase in time scales is not in proportion to the corresponding increase in the conventional viscous time scale $\nu/u_\tau^2$. It is found that the Taylor time scale is most appropriate to describe the essential characteristics of non-equilibrium adverse pressure gradient flows. Even the near wall-limiting behavior of streamwise velocity fluctuations for different $P^+$ is well correlated in the coordinates based on the Taylor time scale. Moreover, in the boundary layer with an adverse pressure gradient, the contribution of sweep motions becomes equivalent to that of ejections, and outward and wallward interactions relatively increase near the wall, which evidently indicates a change in coherent structures.
122679168
Large-scale turbulent structure of uniform shallow free-surface flows
The hydrodynamics of super- and sub-critical shallow uniform free-surface flows are assessed using laboratory experiments aimed at identifying and quantifying flow structure at scales larger than the flow depth. In particular, we provide information on probability distributions of horizontal velocity components, their correlation functions, velocity spectra, and structure functions for the near-water-surface flow region. The data suggest that for the high Froude number flows the structure of the near-surface layer resembles that of two-dimensional turbulence with an inverse energy cascade. In contrast, although large-scale velocity fluctuations were also present in low Froude number flow its behaviour was different, with a direct energy cascade. Based on our results and some published data we suggest a physical explanation for the observed behaviours. The experiments support Jirka’s [Jirka GH (2001) J Hydraul Res 39(6):567–573] hypothesis that secondary instabilities of the base flow may generate large-scale two-dimensional eddies, even in the absence of transverse gradients in the time-averaged flow properties.
128327884
Effects of Adverse Pressure Gradients on Mean Flows and Turbulence Statistics in a Boundary Layer
Measurements in boundary layers with ‘moderate’ to ‘strong’ adverse pressure gradients are presented and discussed. With increasing adverse pressure gradients, the velocity profile in \( {\overline U ^ + } \sim {y^ + }\) coordinates lies below the standard log law, thus indicating a reduction in the thickness of the sublayer. Correspondingly, the turbulence energy components as well as the Reynolds shear stress peak in the outer region of the boundary layer. Higher-order moments of velocity fluctuations are also seriously affected by the adverse pressure gradient. In strong adverse-pressure-gradient flows, the triple products of velocity have completely opposite signs to those in zero-pressure-gradient flows over most of the boundary layer.
39593433
Study of the near-wall-turbulent region of the high-Reynolds-number boundary layer using an atmospheric flow
Data from the near-wall-turbulent region of the high-Reynolds-number atmospheric surface layer are used to analyse the attached-eddy model of wall turbulence. All data were acquired during near-neutral conditions at the Surface Layer Turbulence and Environmental Science Test (SLTEST) facility located in the western Utah Great Salt Lake Desert. Instantaneous streamwise and wall-normal components of velocity were collected with a wall-normal array of two-component hot wires within the first 2 m above the surface of the salt flats. Streamwise and wall-normal turbulence intensities and spectra are directly compared to corresponding laboratory data and similarity formulations hypothesized from the attached-eddy model of wall turbulence. This affords the opportunity to compare results with Reynolds numbers varying over three orders of magnitude. The wall-normal turbulence-intensity similarity formulation is extended. The results show good support for the similarity arguments forwarded by the attached-eddy model as well as Townsend's (1956) Reynolds-number similarity hypothesis and lack of the ‘inactive’ motion influence on the wall-normal velocity component. The effects of wall roughness and the spread in the convection velocity due to this roughness are also discussed.
35823158
Wall turbulence closure based on classical similarity laws and the attached eddy hypothesis
A new look at the closure problem of turbulent boundary layers is taken here using recently derived analytical expressions for the shear stress distributions. These expressions are based on the logarithmic law of the wall and law of the wake formulation of Coles [J. Fluid Mech. 1, 191 (1956)] with the mean continuity and the mean momentum differential and integral equations. The concept of equilibrium layers of Clauser [Adv. Mech. 4, 1 (1956)] is extended and using similar ideas as Rotta [Prog. Aeronaut. Sci. 2, 1 (1962)] for self‐similarity, a closure scheme is proposed for layers developing in arbitrary pressure gradients for the case where the streamwise derivative of the Coles wake factor is not too large. For a given flow case, this Coles wake condition can be tested with internal consistency checks. The mathematical framework is most suitable for incorporating Townsend’s attached eddy hypothesis as recently developed by Perry, Li, and Marusic [Philos. Trans. R. Soc. London Ser. A 336, 67 (1991)] for closure. This gives an opportunity to incorporate coherent structure concepts into closure schemes. Possible ways of handling the difficult case where the streamwise derivative of the Coles wake factor is significant are discussed.
39413543
On the streamwise evolution of turbulent boundary layers in arbitrary pressure gradients
A new approach to the classic closure problem for turbulent boundary layers is presented. This involves, first, using the well-known mean-flow scaling laws such as the log law of the wall and the law of the wake of Coles (1956) together with the mean continuity and the mean momentum differential and integral equations. The important parameters governing the flow in the general non-equilibrium case are identified and are used for establishing a framework for closure. Initially closure is achieved here empirically and the potential for achieving closure in the future using the wall-wake attached eddy model of Perry & Marusic (1995) is outlined. Comparisons are made with experiments covering adverse-pressure-gradient flows in relaxing and developing states and flows approaching equilibrium sink flow. Mean velocity profiles, total shear stress and Reynolds stress profiles can be computed for different streamwise stations, given an initial upstream mean velocity profile and the streamwise variation of free-stream velocity. The attached eddy model of Perry & Marusic (1995) can then be utilized, with some refinement, to compute the remaining unknown quantities such as Reynolds normal stresses and associated spectra and cross-power spectra in the fully turbulent part of the flow.
122768659
Coherent Motions in the Turbulent Boundary Layer
The role of coherent structures in the production and dissipation of turbulence in a boundary layer is characterized, summarizing the results of recent investigations. Coherent motion is defined as a three-dimensional region of flow where at least one fundamental variable exhibits significant correlation with itself or with another variable over a space or time range significantly larger than the smallest local scales of the flow. Sections are then devoted to flow-visualization experiments, statistical analyses, numerical simulation techniques, the history of coherent-structure studies, vortices and vortical structures, conceptual models, and predictive models. Diagrams and graphs are provided.
119883562
Reynolds-number scaling of the flat-plate turbulent boundary layer
Despite extensive study, there remain significant questions about the Reynolds-number scaling of the zero-pressure-gradient flat-plate turbulent boundary layer. While the mean flow is generally accepted to follow the law of the wall, there is little consensus about the scaling of the Reynolds normal stresses, except that there are Reynolds-number effects even very close to the wall. Using a low-speed, high-Reynolds-number facility and a high-resolution laser-Doppler anemometer, we have measured Reynolds stresses for a flat-plate turbulent boundary layer from Reθ = 1430 to 31 000. Profiles of u′2, v′2, and u′v′ show reasonably good collapse with Reynolds number: u′2 in a new scaling, and v′2 and u′v′ in classic inner scaling. The log law provides a reasonably accurate universal profile for the mean velocity in the inner region.
122194594
The effects of a favourable pressure gradient and of the Reynolds number on an incompressible axisymmetric turbulent boundary layer - Part 1. The turbulent boundary layer
The effects of a favourable pressure gradient ( K [les ]4×10 −6 ) and of the Reynolds number
 (862[les ] Re δ 2 [les ]5800) on the mean
 and fluctuating quantities of four turbulent boundary layers were studied experimentally and are presented in this paper
 and a companion paper (Part 2). The measurements consist of extensive hot-wire
 and skin-friction data. The former comprise mean and fluctuating velocities, their correlations
 and spectra, the latter wall-shear stress measurements obtained by four
 different techniques which allow testing of calibrations in both laminar-like and
 turbulent flows for the first time. The measurements provide complete data sets,
 obtained in an axisymmetric test section, which can serve as test cases as specified
 by the 1981 Stanford conference. Two different types of accelerated boundary layers were investigated
 and are described: in this paper (Part 1) the fully turbulent, accelerated boundary
 layer (sometimes denoted laminarescent) with approximately local equilibrium
 between the production and dissipation of the turbulent energy and with relaxation
 to a zero pressure gradient flow (cases 1 and 3); and in Part 2 the strongly accelerated
 boundary layer with ‘inactive’ turbulence, laminar-like mean flow behaviour
 (relaminarized), and reversion to the turbulent state (cases 2 and 4). In all four cases
 the standard logarithmic law fails but there is no single parametric criterion which
 denotes the beginning or the end of this breakdown. However, it can be demonstrated
 that the departure of the mean-velocity profile is accompanied by characteristic
 changes of turbulent quantities, such as the maxima of the Reynolds stresses or the
 fluctuating value of the skin friction. The boundary layers described here are maintained in the laminarescent
 state just up to the beginning of relaminarization and then relaxed to the turbulent
 state in a zero pressure gradient. The relaxation of the turbulence structure occurs
 much faster than in an adverse pressure gradient. In the accelerating boundary layer
 absolute values of the Reynolds stresses remain more or less constant in the outer
 region of the boundary layer in accordance with the results of Blackwelder &
 Kovasznay (1972), and rise both in the vincinity of the wall in conjunction with the rising
 wall shear stress and in the centre region of the boundary layer with the increase
 of production.
123070168
An experimental investigation of a highly accelerated turbulent boundary layer
A canonical flat-plate turbulent boundary layer with Reθ = 4590 is exposed to a favourable mean streamwise pressure gradient sufficient to cause relaminarization. The favourable pressure gradient is generated by a linear contraction, yielding a peak value of the acceleration parameter of K = 4.4 × 10−6 which is sustained for approximately 13 local boundary layer thicknesses. The relaminarization process is characterized by an extensive series of mean flow and turbulence measurements obtained at several representative streamwise locations. In anticipation of the loss of standard log-law behaviour, the local wall shear stress is directly measured using the oil-film interferometry technique. Mean flow measurements show a systematic variation in the Kármán and additive constants with applied streamwise strain rate. The series of measurements also indicate an apparent decoupling of the outer and near-wall regions of the accelerating boundary layer. In accord with this, conditional measurements show that fourth-quadrant sweep events are virtually eliminated, while much less frequent but larger-amplitude near-wall second-quadrant ejection events remain. The reduction in fourth-quadrant sweep events is matched by an observed increase in near-wall third-quadrant events. The consequent reduction in near-wall Reynolds stress correlation and associated cross-stream momentum transport results in a large reduction in cf for the relaminarized flow.
2048797
Direct Numerical Simulation of Self-Similar Turbulent Boundary Layers in Adverse Pressure Gradients
Direct numerical simulations of the Navier–Stokes equations have been carried out with the objective of studying turbulent boundary layers in adverse pressure gradients. The boundary layer flows concerned are of the equilibrium type which makes the analysis simpler and the results can be compared with earlier experiments and simulations. This type of turbulent boundary layers also permits an analysis of the equation of motion to predict separation. The linear analysis based on the assumption of asymptotically high Reynolds number gives results that are not applicable to finite Reynolds number flows. A different non-linear approach is presented to obtain a useful relation between the freestream variation and other mean flow parameters. Comparison of turbulent statistics from the zero pressure gradient case and two adverse pressure gradient cases shows the development of an outer peak in the turbulent energy in agreement with experiment. The turbulent flows have also been investigated using a differential Reynolds stress model. Profiles for velocity and turbulence quantities obtained from the direct numerical simulations were used as initial data. The initial transients in the model predictions vanished rapidly. The model predictions are compared with the direct simulations and low Reynolds number effects are investigated.
120086708
Turbulence development in a non-equilibrium turbulent boundary layer with mild adverse pressure gradient
High-resolution laser-Doppler anemometer measurements were acquired in a two-dimensional turbulent boundary layer over a $4^\circ$ ramp. The goals were to provide a detailed data set for an adverse pressure gradient boundary layer far from separation and to examine near-wall behaviour of the Reynolds stresses as compared to flat-plate boundary layers. The flow develops over a flat plate, reaching a momentum thickness Reynolds number of 3350 at an upstream reference location. The boundary layer is then subjected to a varying pressure gradient along the length of the ramp and partially redevelops on a downstream flat plate. Mean velocity measurements show a log law region in all velocity profiles, but the outer layer does not collapse in deficit coordinates indicating that the boundary layer is not in equilibrium. Measurements of non-dimensional stress ratios and quadrant analysis of the two-component data indicate relatively small changes to the turbulence structure. However, the streamwise normal stress has an extended outer layer plateau, and the shear stress and wall-normal stress have outer layer peaks. Near the wall, the streamwise normal stress and shear stress collapse with flat-plate data using standard scaling, but the wall normal stress is substantially larger than flat-plate cases.
34455766
High Reynolds number effects in wall turbulence
A review of recent advances in the study of high Reynolds number turbulent boundary layers is given. The emergent regime of very large-scale structures in the logarithmic region and their subsequent influence on the near-wall cycle challenges many of the previously held assumptions regarding scaling of turbulent boundary layers at high Reynolds numbers. Experimental results are presented to illustrate the superimposition of large-scale energy onto the near-wall cycle, together with an interaction well described by an amplitude modulation effect. Both phenomena are shown to increase in magnitude (as compared to viscous-scaled events) as Reynolds number increases. These observations lead to a possible model for a statistically representative near-wall velocity signal (giving accurate energy spectra) based on a given filtered velocity signal from the log region of a high Reynolds number turbulent flow.
18508851
Vortex organization in the outer region of the turbulent boundary layer
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 < Reθ < 6845 show that the boundary layer is densely populated by velocity fields associated with hairpin vortices. (The term ‘hairpin’ is here taken to represent cane, hairpin, horseshoe, or omega-shaped vortices and deformed versions thereof, recognizing these structures are variations of a common basic flow structure at different stages of evolution and with varying size, age, aspect ratio, and symmetry.) The signature pattern of the hairpin consists of a spanwise vortex core located above a region of strong second-quadrant fluctuations (u < 0 and v > 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.
12795978
Large- and very-large-scale motions in channel and boundary-layer flows
Large-scale motions (LSMs; having wavelengths up to 2–3 pipe radii) and very-LSMs (having wavelengths more than 3 pipe radii) have been shown to carry more than half of the kinetic energy and Reynolds shear stress in a fully developed pipe flow. Studies using essentially the same methods of measurement and analysis have been extended to channel and zero-pressure-gradient boundary-layer flows to determine whether large structures appear in these canonical wall flows and how their properties compare with that of the pipe flow. The very large scales, especially those of the boundary layer, are shorter than the corresponding scales in the pipe flow, but otherwise share a common behaviour, suggesting that they arise from similar mechanism(s) aside from the modifying influences of the outer geometries. Spectra of the net force due to the Reynolds shear stress in the channel and boundary layer flows are similar to those in the pipe flow. They show that the very-large-scale and main turbulent motions act to decelerate the flow in the region above the maximum of the Reynolds shear stress.
121988281
The structure of turbulent boundary layers
Extensive visual and quantitative studies of turbulent boundary layers are described. Visual studies reveal the presence of surprisingly well-organized spatially and temporally dependent motions within the so-called ‘laminar sublayer’. These motions lead to the formation of low-speed streaks in the region very near the wall. The streaks interact with the outer portions of the flow through a process of gradual ‘lift-up’, then sudden oscillation, bursting, and ejection. It is felt that these processes play a dominant role in the production of new turbulence and the transport of turbulence within the boundary layer on smooth walls. Quantitative data are presented providing an association of the observed structure features with the accepted ‘regions’ of the boundary layer in non-dimensional co-ordinates; these data include zero, negative and positive pressure gradients on smooth walls. Instantaneous spanwise velocity profiles for the inner layers are given, and dimensionless correlations for mean streak-spacing and break-up frequency are presented. Tentative mechanisms for formation and break-up of the low-speed streaks are proposed, and other evidence regarding the implications and importance of the streak structure in turbulent boundary layers is reviewed.
123514548
Estimation of turbulent convection velocities and corrections to Taylor's approximation
A new method is introduced for estimating the convection velocity of individual modes in turbulent shear flows that, in contrast to most previous ones, only requires spectral information in the temporal or spatial direction over which a modal decomposition is desired, while only using local derivatives in other directions. If no spectral information is desired, the method provides a natural definition for the average convection velocity, as well as a way to estimate the accuracy of the frozen-turbulence approximation. Existing data from numerical turbulent channels at friction Reynolds numbers Reτ ≤ 1900 are used to validate the new method against classical ones, and to characterize the dependence of the convection velocity on the eddy wavelength and wall distance. The results indicate that the small scales in turbulent channels travel at the local mean velocity, while large ‘global’ modes travel at a more uniform speed proportional to the bulk velocity. To estimate the systematic deviations introduced in experimental spectra by the use of Taylor's approximation with a wavelength-independent convection velocity, a semi-empirical fit to the computed convection velocities is provided. It represents well the data throughout the Reynolds number range of the simulations. It is shown that Taylor's approximation not only displaces the large scales near the wall to shorter apparent wavelengths but also modifies the shape of the spectrum, giving rise to spurious peaks similar to those observed in some experiments. To a lesser extent the opposite is true above the logarithmic layer. The effect increases with the Reynolds number, suggesting that some of the recent challenges to the kx−1 energy spectrum may have to be reconsidered.
38276008
Large-eddy simulation of large-scale structures in long channel flow
We investigate statistics of large-scale structures from large-eddy simulation (LES) of turbulent channel flow at friction Reynolds numbers Reτ = 2K and 200K (where K denotes 1000). In order to capture the behaviour of large-scale structures properly, the channel length is chosen to be 96 times the channel half-height. In agreement with experiments, these large-scale structures are found to give rise to an apparent amplitude modulation of the underlying small-scale fluctuations. This effect is explained in terms of the phase relationship between the large- and small-scale activity. The shape of the dominant large-scale structure is investigated by conditional averages based on the large-scale velocity, determined using a filter width equal to the channel half-height. The conditioned field demonstrates coherence on a scale of several times the filter width, and the small-scale–large-scale relative phase difference increases away from the wall, passing through π/2 in the overlap region of the mean velocity before approaching π further from the wall. We also found that, near the wall, the convection velocity of the large scales departs slightly, but unequivocally, from the mean velocity.
123123562
On the limitations of Taylor's hypothesis in constructing long structures in a turbulent boundary layer
Taylor's hypothesis of frozen flow has frequently been used to convert temporal experimental measurements into a spatial domain. This technique has led to the discovery of long meandering structures in the log-region of a turbulent boundary layer. There is some contention over whether Taylor's approximation is valid over large distances. This paper presents an experiment that compares velocity fields constructed using Taylor's approximation with those obtained from particle image velocimetry (PIV), i.e. spatial data, obtained in the logarithmic region of a turbulent boundary layer.
122339983
Self-Similarity in the Outer Region of Adverse-Pressure-Gradient Turbulent Boundary Layers
This paper presents a consistent theory of self-similarity and of equilibrium in the outer region of turbulent boundary layers that explains recent experimental findings on the subject, including new ones presented here. The theory is first presented in a general form where the outer scales are left unspecified and it is not assumed that the mean velocity defect and the Reynolds stresses share a common velocity scale. It is shown that the main results of the traditional similarity theory remain valid even in this case. Common outer scaling with the Zagarola-Smits length and velocity scales is then chosen. A new pressure gradient parameter is introduced to characterize the local effect of the pressure gradient in all flow conditions including strong adverse-pressure-gradient conditions. By analyzing several adverse-pressure-gradient flow cases, it is shown that self-similarity of the mean velocity defect profile is reached in all cases in localized but significant flow regions. The same is, however, not true of the Reynolds stress profiles. In agreement with the similarity analysis, the self-similar velocity defect profile is found to be a function of the pressure gradient and most flows studied here are only in an approximate state of equilibrium in the region of self-similar defect profiles despite the excellent collapse of the profiles.