Structures In Turbulent Shear Flows Research Articles

Vertical coherence of coherent structures during sand and dust storms: A multi-height synchronous observation study

An experiment was conducted on the Qingtu Lake Observation Array (QLOA) to measure wind and dust information at various wall-normal heights during the sand and dust storm (SDS) process. According to the indicators of the non-stationary features in the flow field, the SDS process can be divided into three stages: ascending, stabilizing, and descending. Based on this division, the Hilbert–Huang transform (HHT) is employed to extract dominant flow structures, which carries a significant portion of the turbulent kinetic energy. Moreover, the HHT spectrum of stream-wise velocity component reveals that the scales of the dominant structures are approximately hundreds of meters in the horizontal direction, and hence suggests the presence of large and very large-scale coherence during the SDS. The hypotheses of Townsend [The Structure of Turbulent Shear Flow (Cambridge University Press, 1976)] and Davenport [“The spectrum of horizontal gustiness near the ground in high winds,” Q. J. R. Meteorol. Soc. 87, 194–211 (1961)] are utilized to demonstrate the vertical coherence of turbulence, which suggests the wall-similarity and evolution of inner/outer interactions for coherent structures during the SDS. Finally, the coherence spectrum [γL2=exp(−2c1Δz/λx)] and the linear transfer kernel [|HL2|=exp(d1−d2Δz/λx)] are parameterized, where c1, d1, d2 are fitting parameters, Δz is wall-normal offset, and λx refers to streamwise wavelength, to illustrate the evolution of the interactions between near-wall and outer regions during the SDS, which highlights the strong connections during the stabilizing stage. In general, the present study analyzed horizontal and wall-normal structures for a comprehensive SDS process, and thus, these findings present abundant features of wall-attached eddies which further be used to improve/enrich existing near-wall models.

Prediction of vortex precession in the draft tube of a model hydro turbine using mean field stability theory and stochastic modelling

In this work we employ mean field stability theory (MFST) to predict the onset of the precessing vortex core (PVC) in the draft tube of Francis turbines. MFST is based on the linear stability analysis of the mean field of turbulent flows. Recent work shows that MFST very accurately predicts the formation of coherent structures in turbulent shear flows, such as the PVC. MFST may further reveal the flow regions that are most susceptible to flow actuation to suppress the PVC, which is of great practical relevance. In this work, MFST is accompanied by a data-driven approach to predict the linear growth rate of the PVC based on pointwise wall pressure measurements. The method is based on statistical evaluation of the probability density function of the PVC amplitude at limit cycle. It makes use of the intense noise induced by the background turbulence, which is expected to be a major driver of hydrodynamic instabilities. The empirical and analytic results are compared to phase-locked LDV measurements conducted inside the draft tube at various operating conditions, to assess the quantitative accuracy of the approach. The methodologies outlined in this work will be of relevance for future design of hydro turbines to run stable over a wide range of operating conditions.

The mean logarithm emerges with self-similar energy balance

Abstract

Wall-attached and wall-detached eddies in wall-bounded turbulent flows

According to Townsend’s attached eddy hypothesis (AEH), a boundary layer flow is comprised of wall-attached eddies, but to extract the part of the flow whose statistical behaviours are well described by the AEH is not at all straightforward. The objective of this work is to extract the part of the flow that can be described by the AEH, and study the statistical behaviours of the other part, which cannot be described by the AEH. In this process, two types of eddies are identified in addition to the Kolmogorov-scale eddies, i.e. wall-attached eddies and wall-detached eddies. The statistical behaviours of the wall-attached eddies are shown to be very well described by the AEH, i.e. the eddies are wall-attached, self-similar and, importantly, Gaussian, whereas the wall-detached eddies cannot be modelled by the AEH. Specifically, a decomposition scheme is proposed following Townsend (The Structure of Turbulent Shear Flow, Cambridge University Press, 1976). We apply our decomposition scheme to three different flows, i.e. channel, boundary layer and atmospheric surface layer flows. The results are similar with only quantitative differences, suggesting possible universality in both the wall-attached eddies and the wall-detached eddies.

Turbulence structures over realistic and synthetic wall roughness in open channel flow at Reτ = 1000

ABSTRACTTurbulence structures in flow over three types of wall roughness: sand-grain, cube roughness and a realistic, multi-scale turbine-blade roughness, are compared to structures observed in flow over a smooth wall in open channel flow at , using direct numerical simulations. Two-point velocity correlations, length scales, inclination angles, and velocity spectra are analysed, and the applicability of Townsend's outer layer similarity hypothesis [Townsend. The structure of turbulent shear flow. Cambridge: Cambridge University Press; 1976] to these parameters was examined. Results from linear stochastic estimation suggest that, near the wall, the quasi-streamwise vortices observed in smooth-wall flow are present in the large-scale recessed regions of multi-scale roughness, whereas they are replaced by a pair of ‘head-up, head-down’ horseshoe structures in sandgrain and cube roughness, similar to those observed by Talapatra and Katz [Coherent structures in the inner part of a rough-wall channel flow resolved using holographic PIV. J Fluid Mech. 2012;711:161–170]. The configuration of conditional eddies near the wall suggests that the kinematical process of vortices differ for each kind of rough surface. Eddies over multiscale roughness are conjectured to obey a growth mechanism similar to those over smooth walls, while around the cube roughness the head-down horse-shoe vortices of Talapatra and Katz [Coherent structures in the inner part of a rough-wall channel flow resolved using holographic PIV. J Fluid Mech. 2012;711:161–170] may undergo solid-body rotation on top of a cube roughness on account of the strong shear layer, shortening the longitudinal extent of near-wall structure and promoting turbulence production during this process. These results illustrate the sensitivity of turbulence structure to the roughness texture, particularly within the roughness sublayer.

Data-driven decomposition of the streamwise turbulence kinetic energy in boundary layers. Part 1. Energy spectra

In wall-bounded turbulence, a multitude of coexisting turbulence structures form the streamwise velocity energy spectrum from the viscosity- to the inertia-dominated range of scales. Definite scaling-trends for streamwise spectra have remained empirically elusive, although a prominent school of thought stems from the works of Perry and Abell (J. Fluid Mech., vol. 79, 1977, pp. 785-799) and Perry et al. (J. Fluid Mech., vol. 165, 1986, pp. 163-199), which were greatly inspired by the attached-eddy hypothesis of Townsend (The Structure of Turbulent Shear Flow, Cambridge University Press, 1976). In this paper, we re-examine the turbulence kinetic energy of the streamwise velocity component in the context of the spectral decompositions of Perry and coworkers. Two universal spectral filters are derived via spectral coherence analysis of two-point velocity signals, spanning a Reynolds number range $Re_\tau \sim \mathcal{O}(10^3)$ to $\mathcal{O}(10^6)$ and form the basis for our decomposition of the logarithmic-region turbulence into stochastically wall-detached and wall-attached portions of energy. The latter is composed of scales larger than a streamwise/wall-normal ratio of $\lambda_x/z \approx 14$. If the decomposition is accepted, a $k_x^{-1}$ scaling region can only appear for $Re_\tau \geq 80\,000$, at a wall-normal position of $z^+ = 100$. Following Perry and co-workers, it is hypothesized that spectral contributions from turbulence structures other than attached eddies obscure a $k_x^{-1}$ scaling. When accepting the idea of different spectral contributions it is furthermore shown that a broad outer-spectral peak is present even at low $Re_\tau$.

Characteristic scales of Townsend's wall-attached eddies.

Townsend (The Structure of Turbulent Shear Flow, 1976, Cambridge University Press) proposed a structural model for the logarithmic layer (log layer) of wall turbulence at high Reynolds numbers, where the dominant momentum-carrying motions are organised into a multiscale population of eddies attached to the wall. In the attached-eddy framework, the relevant length and velocity scales of the wall-attached eddies are the friction velocity and the distance to the wall. In the present work, we hypothesise that the momentum-carrying eddies are controlled by the mean momentum flux and mean shear with no explicit reference to the distance to the wall and propose new characteristic velocity, length and time scales consistent with this argument. Our hypothesis is supported by direct numerical simulation of turbulent channel flows driven by non-uniform body forces and modified mean velocity profiles, where the resulting outer-layer flow structures are substantially altered to accommodate the new mean momentum transfer. The proposed scaling is further corroborated by simulations where the no-slip wall is replaced by a Robin boundary condition for the three velocity components, allowing for substantial wall-normal transpiration at all length scales. We show that the outer-layer one-point statistics and spectra of this channel with transpiration agree quantitatively with those of its wall-bounded counterpart. The results reveal that the wall-parallel no-slip condition is not required to recover classic wall-bounded turbulence far from the wall and, more importantly, neither is the impermeability condition at the wall.

Hierarchical random additive model for wall-bounded flows at high Reynolds numbers

High Reynolds number wall-bounded flows involve dynamically important scales that cover many orders of magnitude in time and space. Fluid motions that dominate momentum transport also cover wide ranges of scales and all of these scales must be accounted for when modeling turbulence near walls. In this review, we summarize recent developments as related to the so-called hierarchical random additive process (HRAP), which models the near-wall momentum-carrying parts of turbulence by exploiting the self-similarity and the tree-like hierarchical organization of attached eddies. The HRAP model follows Townsend (1980 The Structure of Turbulent Shear Flow) and models boundary layer flows as collections of space-filling, self-similar, wall-attached eddies. However, instead of invoking specifically-shaped typical eddy, HRAP isolates the basic scaling properties of the phenomena by parameterizing contributions of near-wall eddies to generic flow quantities using random addends, a superposition of which leads to the real observable (fluid velocity, wall-shear stress, etc). This compact and relatively simple representation proves to be quite useful, leading to scaling predictions of many turbulence statistics. So far, the HRAP model has been used to provide estimates for scalings of single- and two-point velocity central moments, single- and two-point moment generating functions of velocity fluctuations, and variance of wall-shear stress fluctuations as a function of Reynolds number.

Fractality and the law of the wall.

Fluid motions in the inertial range of isotropic turbulence are fractal, with their space-filling capacity slightly below regular three-dimensional objects, which is a consequence of the energy cascade. Besides the energy cascade, the other often encountered cascading process is the momentum cascade in wall-bounded flows. Despite the long-existing analogy between the two processes, many of the thoroughly investigated aspects of the energy cascade have so far received little attention in studies of the momentum counterpart, e.g., the possibility of the momentum-transferring scales in the logarithmic region being fractal has not been considered. In this work, this possibility is pursued, and we discuss one of its implications. Following the same dimensional arguments that lead to the D=2.33 fractal dimension of wrinkled surfaces in isotropic turbulence, we show that the large-scale momentum-carrying eddies may also be fractal and non-space-filling, which then leads to the power-law scaling of the mean velocity profile. The logarithmic law of the wall, on the other hand, corresponds to space-filling eddies, as suggested by Townsend [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, 1980)]. Because the space-filling capacity is an integral geometric quantity, the analysis presented in this work provides us with a low-order quantity, with which, one would be able to distinguish between the logarithmic law and the power law.

Nonlinear optimal large-scale structures in turbulent channel flow

Coherent structures in turbulent shear flows take the form of packets of hairpin vortices reaching the outer region of the boundary layer along with streaks of different size, going from the near-wall to the outer region. The latter can be explained by the linear transient growth of the perturbations of the mean turbulent profile. Whereas, the former are recently found to be optimally-growing only in the presence of nonlinear effects, as ascertained for a turbulent channel flow at a low friction Reynolds number. The present work aims at investigating whether large-scale streaks can be optimally-growing in a nonlinear framework for a turbulent channel flow. Changing the friction Reynolds number from 180 to 590, the nonlinear optimal perturbation tends towards more robust large-scale streaks and vortical structures of smaller size. These streaks are generated by a coherent large-scale lift-up mechanism, acting as a source term in the energy balance, inducing a positive turbulent kinetic energy production at the outer scale. This indicates that the outer energy production peak arising between the two considered Reynolds numbers can be associated with the growth of optimal large-scale streaks, which represent a robust feature of turbulent channel flows.

Applicability of Taylor’s hypothesis in rough- and smooth-wall boundary layers

The spatial structure of smooth- and rough-wall boundary layers is examined spectrally at approximately matched friction Reynolds number ($\unicode[STIX]{x1D6FF}^{+}\approx 12\,000$). For each wall condition, temporal and true spatial descriptions of the same flow are available from hot-wire anemometry and high-spatial-range particle image velocimetry, respectively. The results show that over the resolved flow domain, which is limited to a streamwise length of twice the boundary layer thickness, true spatial spectra of smooth-wall streamwise and wall-normal velocity fluctuations agree, to within experimental uncertainty, with those obtained from time series using Taylor’s frozen turbulence hypothesis (Proc. R. Soc. Lond. A, vol. 164, 1938, pp. 476–490). The same applies for the streamwise velocity spectra on rough walls. For the wall-normal velocity spectra, however, clear differences are observed between the true spatial and temporally convected spectra. For the rough-wall spectra, a correction is derived to enable accurate prediction of wall-normal velocity length scales from measurements of their time scales, and the implications of this correction are considered. Potential violations to Taylor’s hypothesis in flows above perturbed walls may help to explain conflicting conclusions in the literature regarding the effect of near-wall modifications on outer-region flow. In this regard, all true spatial and corrected spectra presented here indicate structural similarity in the outer region of smooth- and rough-wall flows, providing evidence for Townsend’s wall-similarity hypothesis (The Structure of Turbulent Shear Flow, vol. 1, 1956).

Comparison of turbulent boundary layers over smooth and rough surfaces up to high Reynolds numbers

Turbulent boundary layer measurements above a smooth wall and sandpaper roughness are presented across a wide range of friction Reynolds numbers, ${\it\delta}_{99}^{+}$, and equivalent sand grain roughness Reynolds numbers, $k_{s}^{+}$ (smooth wall: $2020\leqslant {\it\delta}_{99}^{+}\leqslant 21\,430$, rough wall: $2890\leqslant {\it\delta}_{99}^{+}\leqslant 29\,900$; $22\leqslant k_{s}^{+}\leqslant 155$; and $28\leqslant {\it\delta}_{99}^{+}/k_{s}^{+}\leqslant 199$). For the rough-wall measurements, the mean wall shear stress is determined using a floating element drag balance. All smooth- and rough-wall data exhibit, over an inertial sublayer, regions of logarithmic dependence in the mean velocity and streamwise velocity variance. These logarithmic slopes are apparently the same between smooth and rough walls, indicating similar dynamics are present in this region. The streamwise mean velocity defect and skewness profiles each show convincing collapse in the outer region of the flow, suggesting that Townsend’s (The Structure of Turbulent Shear Flow, vol. 1, 1956, Cambridge University Press.) wall-similarity hypothesis is a good approximation for these statistics even at these finite friction Reynolds numbers. Outer-layer collapse is also observed in the rough-wall streamwise velocity variance, but only for flows with ${\it\delta}_{99}^{+}\gtrsim 14\,000$. At Reynolds numbers lower than this, profile invariance is only apparent when the flow is fully rough. In transitionally rough flows at low ${\it\delta}_{99}^{+}$, the outer region of the inner-normalised streamwise velocity variance indicates a dependence on $k_{s}^{+}$ for the present rough surface.

Dissipative distinctions

There have been numerous studies concerning the possibility of self-similar scaling laws in fully developed turbulent shear flows, driven over the past half-century or so by the early seminal work of Townsend (1956, The Structure of Turbulent Shear Flow. Cambridge University Press). His and nearly all subsequent analyses depend crucially on a hypothesis about the nature of the dissipation, ${\it\epsilon}$, of turbulence kinetic energy, $k$. It has usually been assumed (sometimes implicitly) that this is governed by the famous Kolmogorov relation ${\it\epsilon}=C_{{\it\epsilon}}k^{3/2}/L$, where $L$ is a length scale of the energy-containing eddies and $C_{{\it\epsilon}}$ is a constant. The paper by Dairay et al. (J. Fluid Mech. vol. 781, 2015, pp. 166–195) demonstrates, however, that, in the specific context of an axisymmetric wake, there can be regions where ${\it\epsilon}$ has a different behaviour, characterised by a $C_{{\it\epsilon}}$ that is not constant but depends on a varying local Reynolds number (despite the existence of a $-5/3$ region in the spectra). This leads to fundamentally different scaling laws for the wake.

Linear stability of optimal streaks in the log-layer of turbulent channel flows

The importance of secondary instability of streaks for the generation of vortical structures attached to the wall in the logarithmic region of turbulent channels is studied. The streaks and their linear instability are computed by solving equations associated with the organized motion that include an eddy-viscosity modeling the effect of incoherent fluctuations. Three friction Reynolds numbers, Reτ = 2000, 3000, and 5000, are investigated. For all flow cases, optimal streamwise vortices (i.e., having the highest potential for linear transient energy amplification) are used as initial conditions. Due to the lift-up mechanism, these optimal perturbations lead to the nonlinear growth of streaks. Based on a Floquet theory along the spanwise direction, we observe the onset of streak secondary instability for a wide range of spanwise wavelengths when the streak amplitude exceeds a critical value. Under neutral conditions, it is shown that streak instability modes have their energy mainly concentrated in the overlap layer and propagate with a phase velocity equal to the mean streamwise velocity of the log-layer. These neutral log-layer modes exhibit a sinuous pattern and have characteristic sizes that are proportional to the wall distance in both streamwise and spanwise directions, in agreement with the Townsend’s attached eddy hypothesis (A. Townsend, the structure of turbulent shear flow, Cambridge university press, 1976 2nd edition). In particular, for a distance from the wall varying from y+ ≈ 100 (in wall units) to y ≈ 0.3h, where h is half the height of the channel, the neutral log-layer modes are self-similar with a spanwise width of λz ≈ y/0.3 and a streamwise length of λx ≈ 3λz, independently of the Reynolds number. Based on this observation, it is suggested that compact vortical structures attached to the wall can be ascribed to streak secondary instabilities. In addition, spatial distributions of fluctuating vorticity components show that the onset of secondary instability is associated with the roll-up of the shear layer at the edge of the low-speed streak, similarly to a three-dimensional mixing layer.

The streamwise turbulence intensity in the intermediate layer of turbulent pipe flow

The spectral model of Perryet al. (J. Fluid Mech., vol. 165, 1986, pp. 163–199) predicts that the integral length scale varies very slowly with distance to the wall in the intermediate layer. The only way for the integral length scale’s variation to be more realistic while keeping with the Townsend–Perry attached eddy spectrum is to add a new wavenumber range to the model at wavenumbers smaller than that spectrum. This necessary addition can also account for the high-Reynolds-number outer peak of the turbulent kinetic energy in the intermediate layer. An analytic expression is obtained for this outer peak in agreement with extremely high-Reynolds-number data by Hultmarket al. (Phys. Rev. Lett., vol. 108, 2012, 094501;J. Fluid Mech., vol. 728, 2013, pp. 376–395). Townsend’s (The Structure of Turbulent Shear Flows, 1976, Cambridge University Press) production–dissipation balance and the finding of Dallaset al. (Phys. Rev. E, vol. 80, 2009, 046306) that, in the intermediate layer, the eddy turnover time scales with skin friction velocity and distance to the wall implies that the logarithmic derivative of the mean flow has an outer peak at the same location as the turbulent kinetic energy. This is seen in the data of Hultmarket al. (Phys. Rev. Lett., vol. 108, 2012, 094501;J. Fluid Mech., vol. 728, 2013, pp. 376–395). The same approach also predicts that the logarithmic derivative of the mean flow has a logarithmic decay at distances to the wall larger than the position of the outer peak. This qualitative prediction is also supported by the aforementioned data.

Coherent structures and drag-reduction mechanism in wall turbulence

The discovery of coherent structures in turbulent shear flows is one of the most important advances in turbulence research of the last century. These large-scale structures play important role in the physics of wall turbulence, and suggest a new direction for turbulence control. High skin friction in wall-bounded turbulent flows is closely associated with the coherent structures in the near-wall region. The control strategy based on the near-wall physics successfully achieves drag reduction, yet becomes less effective as the Reynolds number increases. It was discovered recently that large-scale coherent motions exist in the outer layer of the high-Reynolds number wall turbulence. These motions have important influence on turbulence in the near-wall region and the skin friction, and bring new challenges to the control of turbulent flow at high Reynolds number. In the present paper, we briefly review the research history on coherent structures in wall turbulence, and mainly focus on dis- cussing the near-wall coherent structures and their control mechanism, the recent research developments on the large-scale motions in the outer region of high-Reynolds number wall turbulence, and the key issues concerning the drag-reduction control of the high-Reynolds number turbulent flows.

Mean flow stability analysis of oscillating jet experiments

AbstractLinear stability analysis (LSA) is applied to the mean flow of an oscillating round jet with the aim of investigating the robustness and accuracy of mean flow stability wave models. The jet’s axisymmetric mode is excited at the nozzle lip through a sinusoidal modulation of the flow rate at amplitudes ranging from 0.1 % to 100 %. The instantaneous flow field is measured via particle image velocimetry (PIV) and decomposed into a mean and periodic part utilizing proper orthogonal decomposition (POD). Local LSA is applied to the measured mean flow adopting a weakly non-parallel flow approach. The resulting global perturbation field is carefully compared with the measurements in terms of spatial growth rate, phase velocity, and phase and amplitude distribution. It is shown that the stability wave model accurately predicts the excited flow oscillations during their entire growth phase and during a large part of their decay phase. The stability wave model applies over a wide range of forcing amplitudes, showing no pronounced sensitivity to the strength of nonlinear saturation. The upstream displacement of the neutral point and the successive reduction of gain with increasing forcing amplitude is very well captured by the stability wave model. At very strong forcing ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{>}40\, \%$), the flow becomes essentially stable to the axisymmetric mode. For these extreme cases, the prediction deteriorates from the measurements due to an interaction of the forced wave with the geometric confinement of the nozzle. Moreover, the model fails far downstream in a region where energy is transferred from the oscillation back to the mean flow. This study supports previously conducted mean flow stability analysis of self-excited flow oscillations in the cylinder wake and in the vortex breakdown bubble and extends the methodology to externally forced convectively unstable flows. The high accuracy of mean flow stability wave models as demonstrated here is of great importance for the analysis of coherent structures in turbulent shear flows.

Zonal detached eddy simulation (ZDES) of a spatially developing flat plate turbulent boundary layer over the Reynolds number range 3 150 ⩽ Reθ ⩽ 14 000

A Wall-Modeled Large Eddy Simulation (WMLES) of a spatially developing zero-pressure gradient smooth flat plate turbulent boundary layer is performed by means of the third mode of the Zonal Detached Eddy Simulation technique. The outer layer is resolved by a Large Eddy Simulation whereas the wall is modeled by a RANS simulation zone, with a RANS/LES interface prescribed at a fixed location. A revisited cost assessment of the Direct Numerical Simulation of high Reynolds numbers (Reθ ⩾ 10 000) wall-bounded flows emphasizes how moderate the cost of the WMLES approach is compared to methods resolving the near-wall dynamics. This makes possible the simulation over a wide Reynolds number range 3 150 ⩽ Reθ ⩽ 14 000, leaving quite enough space for very large scale motions to develop. For a better skin friction prediction, it is shown that the RANS/LES interface should be high enough in the boundary layer and at a location scaling in boundary layer thickness units (e.g., 0.1δ) rather than in wall units. Velocity spectra are compared to experimental data. The outer layer is well resolved, except near the RANS/LES interface where the very simple and robust passive boundary treatment might be improved by a more specific treatment. Besides, the inner RANS zone also contains large scale fluctuations down to the wall. It is shown that these fluctuations fit better to the experimental data for the same interface location that provides a better skin friction prediction. Numerical tests suggest that the observed very large scale motions may appear in an autonomous way, independently from the near-wall dynamics. It still has to be determined whether the observed structures have a physical or a numerical origin. In order to assess how the large scale motions contribute to skin friction, the Reynolds shear stress contribution is studied as suggested by the FIK identity [K. Fukagata, K. Iwamoto, and N. Kasagi, “Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows,” Phys. Fluids 14, L73 (2002)]. Scale decomposition is achieved thanks to the co-spectrum of the Reynolds shear stress in function of the length scale and of the wall distance. The contribution of the large scales to streamwise turbulence intensity and to the Reynolds shear stress is assessed. At the considered Reynolds numbers, the observed largest scales contribute significantly to the Reynolds shear stress in the outer layer but are almost inactive in the sense of Townsend [The Structure of Turbulent Shear Flow (Cambridge University Press, 1976)] closer to the wall. The modeled Cf amounts to only 11% of the total Cf: most of the skin friction is resolved by the present simulations rather than modeled. The large scales, defined by λx > δ, represent the largest contribution to the resolved Cf. It is surmised that there is a correlation between the large scale motions being closer to the experimental data and the better skin friction prediction enabled by a proper interface positioning.

Time-resolved measurements of coherent structures in the turbulent boundary layer

Time-resolved particle image velocimetry was used to examine the structure and evolution of swirling coherent structure (SCS), one interpretation of which is a marker for a three-dimensional coherent vortex structure, in wall-parallel planes of a turbulent boundary layer with a large field of view, 4.3δ × 2.2δ. Measurements were taken at four different wall-normal locations ranging from y/δ = 0.08–0.48 at a friction Reynolds number, Re_τ = 410. The data set yielded statistically converged results over a larger field of view than typically observed in the literature. The method for identifying and tracking swirling coherent structure is discussed, and the resulting trajectories, convection velocities, and lifespan of these structures are analyzed at each wall-normal location. The ability of a model in which the entirety of an individual SCS travels at a single convection velocity, consistent with the attached eddy hypothesis of Townsend (The structure of turbulent shear flows. Cambridge University Press, Cambridge, 1976), to describe the data is investigated. A methodology for determining whether such structures are “attached” or “detached” from the wall is also proposed and used to measure the lifespan and convection velocity distributions of these different structures. SCS were found to persist for longer periods of time further from the wall, particularly those inferred to be “detached” from the wall, which could be tracked for longer than 5 eddy turnover times.

On the logarithmic region in wall turbulence

AbstractConsiderable discussion over the past few years has been devoted to the question of whether the logarithmic region in wall turbulence is indeed universal. Here, we analyse recent experimental data in the Reynolds number range of nominally$2\times 1{0}^{4} \lt {\mathit{Re}}_{\tau } \lt 6\times 1{0}^{5} $for boundary layers, pipe flow and the atmospheric surface layer, and show that, within experimental uncertainty, the data support the existence of a universal logarithmic region. The results support the theory of Townsend (The Structure of Turbulent Shear Flow, Vol. 2, 1976) where, in the interior part of the inertial region, both the mean velocities and streamwise turbulence intensities follow logarithmic functions of distance from the wall.