Earth and Environmental Sciences (23)
Journal of Fluid Mechanics (23)
Ryan Test (23)
Friction factor decomposition for rough-wall flows: theoretical background and application to open-channel flows
V. I. Nikora, T. Stoesser, S. M. Cameron, M. Stewart, K. Papadopoulos, P. Ouro, R. McSherry, A. Zampiron, I. Marusic, R. A. Falconer
Journal: Journal of Fluid Mechanics / Volume 872 / 10 August 2019
Print publication: 10 August 2019
A theoretically based relationship for the Darcy–Weisbach friction factor $f$ for rough-bed open-channel flows is derived and discussed. The derivation procedure is based on the double averaging (in time and space) of the Navier–Stokes equation followed by repeated integration across the flow. The obtained relationship explicitly shows that the friction factor can be split into at least five additive components, due to: (i) viscous stress; (ii) turbulent stress; (iii) dispersive stress (which in turn can be subdivided into two parts, due to bed roughness and secondary currents); (iv) flow unsteadiness and non-uniformity; and (v) spatial heterogeneity of fluid stresses in a bed-parallel plane. These constitutive components account for the roughness geometry effect and highlight the significance of the turbulent and dispersive stresses in the near-bed region where their values are largest. To explore the potential of the proposed relationship, an extensive data set has been assembled by employing specially designed large-eddy simulations and laboratory experiments for a wide range of Reynolds numbers. Flows over self-affine rough boundaries, which are representative of natural and man-made surfaces, are considered. The data analysis focuses on the effects of roughness geometry (i.e. spectral slope in the bed elevation spectra), relative submergence of roughness elements and flow and roughness Reynolds numbers, all of which are found to be substantial. It is revealed that at sufficiently high Reynolds numbers the roughness-induced and secondary-currents-induced dispersive stresses may play significant roles in generating bed friction, complementing the dominant turbulent stress contribution.
Simultaneous skin friction and velocity measurements in high Reynolds number pipe and boundary layer flows
R. Baidya, W. J. Baars, S. Zimmerman, M. Samie, R. J. Hearst, E. Dogan, L. Mascotelli, X. Zheng, G. Bellani, A. Talamelli, B. Ganapathisubramani, N. Hutchins, I. Marusic, J. Klewicki, J. P. Monty
Journal: Journal of Fluid Mechanics / Volume 871 / 25 July 2019
Print publication: 25 July 2019
Streamwise velocity and wall-shear stress are acquired simultaneously with a hot-wire and an array of azimuthal/spanwise-spaced skin friction sensors in large-scale pipe and boundary layer flow facilities at high Reynolds numbers. These allow for a correlation analysis on a per-scale basis between the velocity and reference skin friction signals to reveal which velocity-based turbulent motions are stochastically coherent with turbulent skin friction. In the logarithmic region, the wall-attached structures in both the pipe and boundary layers show evidence of self-similarity, and the range of scales over which the self-similarity is observed decreases with an increasing azimuthal/spanwise offset between the velocity and the reference skin friction signals. The present empirical observations support the existence of a self-similar range of wall-attached turbulence, which in turn are used to extend the model of Baars et al. (J. Fluid Mech., vol. 823, p. R2) to include the azimuthal/spanwise trends. Furthermore, the region where the self-similarity is observed correspond with the wall height where the mean momentum equation formally admits a self-similar invariant form, and simultaneously where the mean and variance profiles of the streamwise velocity exhibit logarithmic dependence. The experimental observations suggest that the self-similar wall-attached structures follow an aspect ratio of $7:1:1$ in the streamwise, spanwise and wall-normal directions, respectively.
A comparative study of the velocity and vorticity structure in pipes and boundary layers at friction Reynolds numbers up to $10^{4}$
S. Zimmerman, J. Philip, J. Monty, A. Talamelli, I. Marusic, B. Ganapathisubramani, R. J. Hearst, G. Bellani, R. Baidya, M. Samie, X. Zheng, E. Dogan, L. Mascotelli, J. Klewicki
Journal: Journal of Fluid Mechanics / Volume 869 / 25 June 2019
Print publication: 25 June 2019
This study presents findings from a first-of-its-kind measurement campaign that includes simultaneous measurements of the full velocity and vorticity vectors in both pipe and boundary layer flows under matched spatial resolution and Reynolds number conditions. Comparison of canonical turbulent flows offers insight into the role(s) played by features that are unique to one or the other. Pipe and zero pressure gradient boundary layer flows are often compared with the goal of elucidating the roles of geometry and a free boundary condition on turbulent wall flows. Prior experimental efforts towards this end have focused primarily on the streamwise component of velocity, while direct numerical simulations are at relatively low Reynolds numbers. In contrast, this study presents experimental measurements of all three components of both velocity and vorticity for friction Reynolds numbers $Re_{\unicode[STIX]{x1D70F}}$ ranging from 5000 to 10 000. Differences in the two transverse Reynolds normal stresses are shown to exist throughout the log layer and wake layer at Reynolds numbers that exceed those of existing numerical data sets. The turbulence enstrophy profiles are also shown to exhibit differences spanning from the outer edge of the log layer to the outer flow boundary. Skewness and kurtosis profiles of the velocity and vorticity components imply the existence of a 'quiescent core' in pipe flow, as described by Kwon et al. (J. Fluid Mech., vol. 751, 2014, pp. 228–254) for channel flow at lower $Re_{\unicode[STIX]{x1D70F}}$ , and characterize the extent of its influence in the pipe. Observed differences between statistical profiles of velocity and vorticity are then discussed in the context of a structural difference between free-stream intermittency in the boundary layer and 'quiescent core' intermittency in the pipe that is detectable to wall distances as small as 5 % of the layer thickness.
Drag forces on a bed particle in open-channel flow: effects of pressure spatial fluctuations and very-large-scale motions
S. M. Cameron, V. I. Nikora, I. Marusic
Journal: Journal of Fluid Mechanics / Volume 863 / 25 March 2019
Print publication: 25 March 2019
The fluctuating drag forces acting on spherical roughness elements comprising the bed of an open-channel flow have been recorded along with synchronous measurements of the surrounding velocity field using stereoscopic particle image velocimetry. The protrusion of the target particle, equipped with a force sensor, was systematically varied between zero and one-half diameter relative to the hexagonally packed adjacent spheres. Premultiplied spectra of drag force fluctuations were found to have bimodal shapes with a low-frequency ( ${\approx}0.5~\text{Hz}$ ) peak corresponding to the presence of very-large-scale motions (VLSMs) in the turbulent flow. The high-frequency ( $\gtrapprox 4~\text{Hz}$ ) region of the drag force spectra cannot be explained by velocity time series extracted from points around the particle, but instead appears to be dominated by the action of pressure gradients in the overlying flow field. For small particle protrusions, this high-frequency region contributes a majority of the drag force variance, while the relative importance of the low-frequency drag force fluctuations increases with increasing protrusion. The amplitude of high-frequency drag force fluctuations is modulated by the VLSMs irrespective of particle protrusion. These results provide some insight into the mechanics of bed particle stability and indicate that the optimum conditions for particle entrainment may occur when a low-pressure region embedded in the high-velocity portion of a VLSM overlays a particle.
Fully resolved measurements of turbulent boundary layer flows up to $Re_{\unicode[STIX]{x1D70F}}=20\,000$
M. Samie, I. Marusic, N. Hutchins, M. K. Fu, Y. Fan, M. Hultmark, A. J. Smits
Journal: Journal of Fluid Mechanics / Volume 851 / 25 September 2018
Fully resolved measurements of turbulent boundary layers are reported for the Reynolds number range $Re_{\unicode[STIX]{x1D70F}}=6000{-}20\,000$ . 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 $Re_{\unicode[STIX]{x1D70F}}=20\,000$ . Results show that in the near-wall region, the viscous-scaled streamwise turbulence intensity grows with $Re_{\unicode[STIX]{x1D70F}}$ 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.
Statistics of turbulence in the energy-containing range of Taylor–Couette compared to canonical wall-bounded flows
Dominik Krug, Xiang I. A. Yang, Charitha M. de Silva, Rodolfo Ostilla-Mónico, Roberto Verzicco, Ivan Marusic, Detlef Lohse
Journal: Journal of Fluid Mechanics / Volume 830 / 10 November 2017
Print publication: 10 November 2017
Considering structure functions of the streamwise velocity component in a framework akin to the extended self-similarity hypothesis (ESS), de Silva et al. (J. Fluid Mech., vol. 823, 2017, pp. 498–510) observed that remarkably the large-scale (energy-containing range) statistics in canonical wall-bounded flows exhibit universal behaviour. In the present study, we extend this universality, which was seen to encompass also flows at moderate Reynolds number, to Taylor–Couette flow. In doing so, we find that also the transversal structure function of the spanwise velocity component exhibits the same universal behaviour across all flow types considered. We further demonstrate that these observations are consistent with predictions developed based on an attached-eddy hypothesis. These considerations also yield a possible explanation for the efficacy of the ESS framework by showing that it relaxes the self-similarity assumption for the attached-eddy contributions. By taking the effect of streamwise alignment into account, the attached-eddy model predicts different behaviour for structure functions in the streamwise and in the spanwise directions and that this effect cancels in the ESS framework – both consistent with the data. Moreover, it is demonstrated here that also the additive constants, which were previously believed to be flow dependent, are indeed universal at least in turbulent boundary layers and pipe flow where high Reynolds number data are currently available.
Applicability of Taylor's hypothesis in rough- and smooth-wall boundary layers
D. T. Squire, N. Hutchins, C. Morrill-Winter, M. P. Schultz, J. C. Klewicki, I. Marusic
Journal: Journal of Fluid Mechanics / Volume 812 / 10 February 2017
Published online by Cambridge University Press: 28 December 2016, pp. 398-417
Print publication: 10 February 2017
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 – ERRATUM
D. T. Squire, C. Morrill-Winter, N. Hutchins, M. P. Schultz, J. C. Klewicki, I. Marusic
Published online by Cambridge University Press: 25 May 2016, p. 917
Comparison of turbulent boundary layers over smooth and rough surfaces up to high Reynolds numbers
Journal: Journal of Fluid Mechanics / Volume 795 / 25 May 2016
Print publication: 25 May 2016
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.
Moment generating functions and scaling laws in the inertial layer of turbulent wall-bounded flows
Xiang I. A. Yang, Ivan Marusic, Charles Meneveau
Published online by Cambridge University Press: 16 February 2016, R2
Properties of single- and two-point moment generating functions (MGFs) are examined in the inertial region of wall-bounded flows. Empirical evidence for power-law scaling of the single-point MGF $\langle \text{exp}(qu^{+})\rangle$ (where $u^{+}$ is the normalized streamwise velocity fluctuation and $q$ a real parameter) with respect to the wall-normal distance is presented, based on hot-wire data from a $Re_{{\it\tau}}=13\,000$ boundary-layer experiment. The parameter $q$ serves as a 'dial' to emphasize different parts of the signal such as high- and low-speed regions, for positive and negative values of $q$ , respectively. Power-law scaling $\langle \text{exp}(qu^{+})\rangle \sim (z/{\it\delta})^{-{\it\tau}(q)}$ can be related to the generalized logarithmic laws previously observed in higher-order moments, such as in $\langle u^{+2p}\rangle ^{1/p}$ , but provide additional information not available through traditional moments if considering $q$ values away from the origin. For two-point MGFs, the scalings in $\langle \text{exp}[qu^{+}(x)+q^{\prime }u^{+}(x+r)]\rangle$ with respect to $z$ and streamwise displacement $r$ in the logarithmic region are investigated. The special case $q^{\prime }=-q$ is of particular interest, since this choice emphasizes rare events with high and low speeds at a distance $r$ . Applying simple scaling arguments motivated by the attached eddy model, a 'scaling transition' is predicted to occur for $q=q_{cr}$ such that ${\it\tau}(q_{cr})+{\it\tau}(-q_{cr})=1$ , where ${\it\tau}(q)$ is the set of scaling exponents for single-point MGFs. This scaling transition is not visible to traditional central moments, but is indeed observed based on the experimental data, illustrating the capabilities of MGFs to provide new and statistically robust insights into turbulence structure and confirming essential ingredients of the attached eddy model.
Evolution of zero-pressure-gradient boundary layers from different tripping conditions
I. Marusic, K. A. Chauhan, V. Kulandaivelu, N. Hutchins
In this paper we study the spatial evolution of zero-pressure-gradient (ZPG) turbulent boundary layers from their origin to a canonical high-Reynolds-number state. A prime motivation is to better understand under what conditions reliable scaling behaviour comparisons can be made between different experimental studies at matched local Reynolds numbers. This is achieved here through detailed streamwise velocity measurements using hot wires in the large University of Melbourne wind tunnel. By keeping the unit Reynolds number constant, the flow conditioning, contraction and trip can be considered unaltered for a given boundary layer's development and hence its evolution can be studied in isolation from the influence of inflow conditions by moving to different streamwise locations. Careful attention was given to the experimental design in order to make comparisons between flows with three different trips while keeping all other parameters nominally constant, including keeping the measurement sensor size nominally fixed in viscous wall units. The three trips consist of a standard trip and two deliberately 'over-tripped' cases, where the initial boundary layers are over-stimulated with additional large-scale energy. Comparisons of the mean flow, normal Reynolds stress, spectra and higher-order turbulence statistics reveal that the effects of the trip are seen to be significant, with the remnants of the 'over-tripped' conditions persisting at least until streamwise stations corresponding to $Re_{x}=1.7\times 10^{7}$ and $x=O(2000)$ trip heights are reached (which is specific to the trips used here), at which position the non-canonical boundary layers exhibit a weak memory of their initial conditions at the largest scales $O(10{\it\delta})$ , where ${\it\delta}$ is the boundary layer thickness. At closer streamwise stations, no one-to-one correspondence is observed between the local Reynolds numbers ( $Re_{{\it\tau}}$ , $Re_{{\it\theta}}$ or $Re_{x}$ etc.), and these differences are likely to be the cause of disparities between previous studies where a given Reynolds number is matched but without account of the trip conditions and the actual evolution of the boundary layer. In previous literature such variations have commonly been referred to as low-Reynolds-number effects, while here we show that it is more likely that these differences are due to an evolution effect resulting from the initial conditions set up by the trip and/or the initial inflow conditions. Generally, the mean velocity profiles were found to approach a constant wake parameter ${\it\Pi}$ as the three boundary layers developed along the test section, and agreement of the mean flow parameters was found to coincide with the location where other statistics also converged, including higher-order moments up to tenth order. This result therefore implies that it may be sufficient to document the mean flow parameters alone in order to ascertain whether the ZPG flow, as described by the streamwise velocity statistics, has reached a canonical state, and a computational approach is outlined to do this. The computational scheme is shown to agree well with available experimental data.
Scaling of second- and higher-order structure functions in turbulent boundary layers
C. M. de Silva, I. Marusic, J. D. Woodcock, C. Meneveau
Journal: Journal of Fluid Mechanics / Volume 769 / 25 April 2015
Print publication: 25 April 2015
The statistical properties of wall turbulence in the logarithmic region are investigated using structure functions of the streamwise velocity. To this end, datasets that span several orders of magnitude of Reynolds numbers are used, up to $Re_{{\it\tau}}=O(10^{6})$ , providing uniquely large scale separations for scrutinising previously proposed scaling laws. For the second-order structure functions strong support is found simultaneously for power-law scalings in the Kolmogorov inertial subrange and for logarithmic scaling at larger scales within the inertial range ( $z<r\ll {\it\delta}$ , where $z$ is the distance from the wall, $r$ the scale, and ${\it\delta}$ the boundary layer thickness). The observed scalings are shown to agree between the datasets, which include both temporal and spatial velocity signals and span from laboratory to atmospheric flows, showing a degree of universality in the results presented. An examination of higher even-order structure functions also shows support for logarithmic scaling behaviour for $z<r\ll {\it\delta}$ , provided that the Reynolds number is sufficiently high. These findings are interpreted by generalising the work of Meneveau & Marusic (J. Fluid Mech., vol. 719, 2013) and introducing bridging relations between higher-order moments of velocity fluctuations and structure functions. Further, a physical model based on the attached-eddy hypothesis is utilised to derive various properties of the structure functions for the energy-containing scales of the logarithmic region. The descriptions derived from the model are shown to be supported by the experimental data.
Reynolds-number-dependent turbulent inertia and onset of log region in pipe flows
C. Chin, J. Philip, J. Klewicki, A. Ooi, I. Marusic
Journal: Journal of Fluid Mechanics / Volume 757 / 25 October 2014
A detailed analysis of the 'turbulent inertia' (TI) term (the wall-normal gradient of the Reynolds shear stress, $\mathrm{d} \langle -uv\rangle /\mathrm{d} y $ ), in the axial mean momentum equation is presented for turbulent pipe flows at friction Reynolds numbers $\delta ^{+} \approx 500$ , 1000 and 2000 using direct numerical simulation. Two different decompositions for TI are employed to further understand the mean structure of wall turbulence. In the first, the TI term is decomposed into the sum of two velocity–vorticity correlations ( $\langle v \omega _z \rangle + \langle - w \omega _y \rangle $ ) and their co-spectra, which we interpret as an advective transport (vorticity dispersion) contribution and a change-of-scale effect (associated with the mechanism of vorticity stretching and reorientation). In the second decomposition, TI is equivalently represented as the wall-normal gradient of the Reynolds shear stress co-spectra, which serves to clarify the accelerative or decelerative effects associated with turbulent motions at different scales. The results show that the inner-normalised position, $y_m^{+}$ , where the TI profile crosses zero, as well as the beginning of the logarithmic region of the wall turbulent flows (where the viscous force is leading order) move outwards in unison with increasing Reynolds number as $y_m^{+} \sim \sqrt{\delta ^{+}}$ because the eddies located close to $y_m^{+}$ are influenced by large-scale accelerating motions of the type $\langle - w \omega _y \rangle $ related to the change-of-scale effect (due to vorticity stretching). These large-scale motions of $O(\delta ^{+})$ gain a spectrum of larger length scales with increasing $\delta ^{+}$ and are related to the emergence of a secondary peak in the $-uv$ co-spectra. With increasing Reynolds number, the influence of the $O(\delta ^{+})$ motions promotes viscosity to act over increasingly longer times, thereby increasing the $y^{+}$ extent over which the mean viscous force retains leading order. Furthermore, the TI decompositions show that the $\langle v \omega _z \rangle $ motions (advective transport and/or dispersion of vorticity) are the dominant mechanism in and above the log region, whereas $\langle - w \omega _y \rangle $ motions (vorticity stretching and/or reorientation) are most significant below the log region. The motions associated with $\langle - w \omega _y \rangle $ predominantly underlie accelerations, whereas $\langle v \omega _z \rangle $ primarily contribute to decelerations. Finally, a description of the structure of wall turbulence deduced from the present analysis and our physical interpretation is presented, and is shown to be consistent with previous flow visualisation studies.
Amplitude modulation of all three velocity components in turbulent boundary layers
K. M. Talluru, R. Baidya, N. Hutchins, I. Marusic
Published online by Cambridge University Press: 31 March 2014, R1
A combination of cross-wire probes with an array of flush-mounted skin-friction sensors are used to study the three-dimensional conditional organisation of large-scale structures in a high-Reynolds-number turbulent boundary layer. Previous studies have documented the amplitude modulation of small-scale motions in response to conditionally averaged large-scale events, but the data are largely restricted to the streamwise component of velocity alone. Here, we report results based on all three components of velocity and find that the small-scale spanwise and wall-normal fluctuations ( $v$ and $w$ ) and the instantaneous Reynolds shear stress ( $-{uw}$ ) are modulated in a very similar manner to that previously noted for the streamwise fluctuations ( $u$ ). The envelope of the small scale fluctuations for all velocity components is well described by the large-scale component of the $u$ fluctuation. These results also confirm the conditional existence of roll modes associated with the very large-scale or 'superstructure' motions.
Obtaining accurate mean velocity measurements in high Reynolds number turbulent boundary layers using Pitot tubes
S. C. C. Bailey, M. Hultmark, J. P. Monty, P. H. Alfredsson, M. S. Chong, R. D. Duncan, J. H. M. Fransson, N. Hutchins, I. Marusic, B. J. McKeon, H. M. Nagib, R. Örlü, A. Segalini, A. J. Smits, R. Vinuesa
Journal: Journal of Fluid Mechanics / Volume 715 / 25 January 2013
Print publication: 25 January 2013
This article reports on one component of a larger study on measurement of the zero-pressure-gradient turbulent flat plate boundary layer, in which a detailed investigation was conducted of the suite of corrections required for mean velocity measurements performed using Pitot tubes. In particular, the corrections for velocity shear across the tube and for blockage effects which occur when the tube is in close proximity to the wall were investigated using measurements from Pitot tubes of five different diameters, in two different facilities, and at five different Reynolds numbers ranging from ${\mathit{Re}}_{\theta } = 11\hspace{0.167em} 100$ to 67 000. Only small differences were found amongst commonly used corrections for velocity shear, but improvements were found for existing near-wall proximity corrections. Corrections for the nonlinear averaging of the velocity fluctuations were also investigated, and the results compared to hot-wire data taken as part of the same measurement campaign. The streamwise turbulence-intensity correction was found to be of comparable magnitude to that of the shear correction, and found to bring the hot-wire and Pitot results into closer agreement when applied to the data, along with the other corrections discussed and refined here.
Estimating wall-shear-stress fluctuations given an outer region input
Romain Mathis, Ivan Marusic, Sergei I. Chernyshenko, Nicholas Hutchins
A model for the instantaneous wall-shear-stress distribution is presented for zero-pressure-gradient turbulent boundary layers. The model, based on empirical and theoretical considerations, is able to reconstruct a statistically representative fluctuating wall-shear-stress time-series, ${ \tau }_{w}^{\ensuremath{\prime} } (t)$ , using only the low-frequency content of the streamwise velocity measured in the logarithmic region, away from the wall. Results, including spectra and second-order moments, show that the model is capable of successfully capturing Reynolds number trends as observed in other studies.
Amplitude and frequency modulation in wall turbulence
B. Ganapathisubramani, N. Hutchins, J. P. Monty, D. Chung, I. Marusic
Journal: Journal of Fluid Mechanics / Volume 712 / 10 December 2012
Published online by Cambridge University Press: 27 September 2012, pp. 61-91
Print publication: 10 December 2012
In this study we examine the impact of the strength of the large-scale motions on the amplitude and frequency of the small scales in high-Reynolds-number turbulent boundary layers. Time series of hot-wire data are decomposed into large- and small-scale components, and the impact of the large scale on the amplitude and frequency of the small scales is considered. The amplitude modulation effect is examined by conditionally averaging the small-scale intensity ( ${ u}_{S}^{2} $ ) for various values of the large-scale fluctuation ( ${u}_{L} $ ). It is shown that ${ u}_{S}^{2} $ increases with increasing value of ${u}_{L} $ in the near-wall region, whereas, farther away from the wall, ${ u}_{S}^{2} $ decreases with increasing ${u}_{L} $ . The rate of increase in small-scale intensity with the strength of the large-scale signal is neither symmetric (about ${u}_{L} = 0$ ) nor linear. The extent of the frequency modulation is examined by counting the number of occurrences of local maxima or minima in the small-scale signal. It is shown that the frequency modulation effect is confined to the near-wall region and its extent diminishes rapidly beyond ${y}^{+ } = 100$ . A phase lag between the large- and small-scale fluctuations, in terms of amplitude modulation, has also been identified, which is in agreement with previous studies. The phase lag between large- and small-scale fluctuations for frequency modulation is comparable to that of amplitude modulation in the near-wall region. The combined effect of both amplitude and frequency modulation is also examined by computing conditional spectra of the small-scale signal conditioned on the large scales. In the near-wall region, the results indicate that the peak value of pre-multiplied spectra increases with increasing value of ${u}_{L} $ , indicating amplitude modulation, while the frequency at which this peak occurs also increases with increasing value of ${u}_{L} $ , revealing frequency modulation. The overall trends observed from the conditional spectra are consistent with the results obtained through statistical analyses. Finally, a physical mechanism that can capture most of the above observations is also presented.
Spatial resolution correction for wall-bounded turbulence measurements
A. J. SMITS, J. MONTY, M. HULTMARK, S. C. C. BAILEY, N. HUTCHINS, I. MARUSIC
A correction for streamwise Reynolds stress data acquired with insufficient spatial resolution is proposed for wall-bounded flows. The method is based on the attached eddy hypothesis to account for spatial filtering effects at all wall-normal positions. This analysis reveals that outside the near-wall region the spatial filtering effect scales inversely with the distance from the wall, in contrast to the commonly assumed scaling with the viscous length scale. The new formulation is shown to work very well for data taken over a wide range of Reynolds numbers and wire lengths.
Three-dimensional conditional structure of a high-Reynolds-number turbulent boundary layer
N. HUTCHINS, J. P. MONTY, B. GANAPATHISUBRAMANI, H. C. H. NG, I. MARUSIC
An array of surface hot-film shear-stress sensors together with a traversing hot-wire probe is used to identify the conditional structure associated with a large-scale skin-friction event in a high-Reynolds-number turbulent boundary layer. It is found that the large-scale skin-friction events convect at a velocity that is much faster than the local mean in the near-wall region (the convection velocity for large-scale skin-friction fluctuations is found to be close to the local mean at the midpoint of the logarithmic region). Instantaneous shear-stress data indicate the presence of large-scale structures at the wall that are comparable in scale and arrangement to the superstructure events that have been previously observed to populate the logarithmic regions of turbulent boundary layers. Conditional averages of streamwise velocity computed based on a low skin-friction footprint at the wall offer a wider three-dimensional view of the average superstructure event. These events consist of highly elongated forward-leaning low-speed structures, flanked on either side by high-speed events of similar general form. An analysis of small-scale energy associated with these large-scale events reveals that the small-scale velocity fluctuations are attenuated near the wall and upstream of a low skin-friction event, while downstream and above the low skin-friction event, the fluctuations are significantly amplified. In general, it is observed that the attenuation and amplification of the small-scale energy seems to approximately align with large-scale regions of streamwise acceleration and deceleration, respectively. Further conditional averaging based on streamwise skin-friction gradients confirms this observation. A conditioning scheme to detect the presence of meandering large-scale structures is also proposed. The large-scale meandering events are shown to be a possible source of the strong streamwise velocity gradients, and as such play a significant role in modulating the small-scale motions.
Universal aspects of small-scale motions in turbulence
G. E. ELSINGA, I. MARUSIC
Two aspects of small-scale turbulence are currently regarded universal, as they have been reported for a wide variety of turbulent flows. Firstly, the vorticity vector has been found to display a preferential alignment with the eigenvector corresponding to the intermediate eigenvalue of the strain rate tensor; and secondly, the joint probability density function (p.d.f.) of the second and third invariant of the velocity gradient tensor, Q and R, has a characteristic teardrop shape. This paper provides an explanation for these universal aspects in terms of a spatial organization of coherent structures, which is based on an evaluation of the average flow pattern in the local coordinate system defined by the eigenvectors of the strain rate tensor. The approach contrasts with previous investigations, which have relied on assumed model flows. The present average flow patterns have been calculated for existing experimental (particle image velocimetry) or numerical (direct numerical simulation) datasets of a turbulent boundary layer (TBL), a turbulent channel flow and for homogeneous isotropic turbulence. All results show a shear-layer structure consisting of aligned vortical motions, separating two larger-scale regions of relatively uniform flow. Because the directions of maximum and minimum strain in a shear layer are in the plane normal to the vorticity vector, this vector aligns with the remaining strain direction, i.e. the intermediate eigenvector of the strain rate tensor. Further, the QR joint p.d.f. for these average flow patterns reveals a shape reminiscent of the teardrop, as seen in many turbulent flows. The above-mentioned organization of the small-scale motions is not only found in the average patterns, but is also frequently observed in the instantaneous velocity fields of the different turbulent flows. It may, therefore, be considered relevant and universal.