Streamwise Velocity Measurements Research Articles

Hot-wire spatial resolution issues in adverse pressure gradient turbulent boundary layers

The effect of a finite length of hot-wire probe sensor length on the measured streamwise velocity fluctuations is well understood in canonical wall-bounded flow, where the small-scale energy has been found to be universal and invariant with Reynolds number. A straightforward application of that assumption to non-canonical flows such as strong adverse pressure gradient (APG) flows has, however, been hampered since the effect of Re and APG could not conclusively be studied separately due to the lack of data with a clear scale separation. The present experimental investigation at Reτ≈4000 in weak, moderate and strong APGs with different wire length shows that spatial averaging effects are not only limited to the inner layer. A note of caution is hence warranted for measurements that seemingly try to take the bias effect of spatial attenuation into account by performing measurements with albeit long but fixed viscous-scaled wire length.

An extended [formula omitted] model for wake-flow simulation of wind farms

The Reynolds-averaged Navier–Stokes approach coupled with the standard k−ɛ model is widely utilized for wind-energy applications. However, it has been shown that the standard k−ɛ model overestimates the turbulence intensity in the wake region and, consequently, overpredicts the power output of the waked turbines. This study focuses on the development of an extended k−ɛ model by incorporating an additional term in the turbulent kinetic energy equation. This term accounts for the influence of turbine-induced forces, and its formulation is derived through an analytical approach. To assess the effectiveness of the proposed model, we begin by analyzing the evolution of normalized velocity deficit and turbulence intensity in the wake region, and the normalized power of the waked turbines. This investigation involves a comparison of the predictions against results from large-eddy simulations in three validation cases with different layouts. We then simulate a wind farm consisting of 30 wind turbines and conduct a comparative analysis between the model-predicted normalized streamwise velocity and wind-tunnel measurements. Finally, to conclude our assessment of the proposed model, we apply it to the operational wind farm of Horns Rev 1 and evaluate the obtained normalized power with the results from large-eddy simulations. The comparisons and validations conducted in this study prove the superior performance of the extended k−ɛ model compared to the standard version.

A study on separation control mechanisms of tandemly arranged wing with linear leading edge and leading edge protuberance

A study on separation control mechanisms of tandemly arranged wing with linear leading edge (LLE) and leading edge protuberance (LEP) in low Reynolds number was conducted. In this study, to investigate the separation control mechanism, we carried out the visualization experiment using smoke-wire method, the streamwise and spanwise velocity measurements above the upper surface of the backward wing by using hotwire anemometer, and the numerical simulation. From the results of flow visualization experiment, it was found that the high lift coefficient obtained by tandemly arranged wing with LLE and singly and tandemly arranged wing with LEP were caused by reducing the flow separation region. From the results of velocity measurements and numerical simulation, it was found that in the case of wing with LLE, the turbulence generated by forward wing, which had mainly streamwise component with peak frequency of 230Hz and broadband frequency over than 30Hz, controled the flow separation. Whereas in the case of wing with LEP, regardless of the wing arrangement, separation control was brought by the separation bubble that caused by the longitudinal vortices generated by the LEP. It was also found that the turbulence from forward wing affected the position of the valley part where the separation bubble and the strong negative pressure were formed.

Influence of boundary layer flow suction on trailing edge noise generation

The effect of uniform inclined flow suction on an equilibrium turbulent boundary layer developing over a flat plate is experimentally investigated for aeroacoustic purposes. Simultaneous measurements of streamwise velocity with hot-wire anemometry, and surface pressure fluctuations using flush-mounted microphones were performed at various locations downstream of the flow control treatment. The paper discusses the effects of flow suction on the turbulent quantities describing the boundary layer, and the associated hydrodynamic pressure field to assess the effects of flow suction on trailing edge noise generation. Two parameters were varied, the inclination of the flow suction velocity (α) and the flow suction severity (σ). The former is the angle of flow suction with respect to the free-stream flow (α = 30°, 50°, 70° and 90°), while the latter is the ratio of momentum deficit within the boundary layer to the momentum of flow suction (σ = 2.5–9.1). Flow suction reduces the height of the boundary layer, which results in an increase of mean shear. The flow energy content within the boundary layer is reduced by suction with the most significant amount of reduction is observed within the logarithmic region. A moderate energy increase is observed in the buffer layer. These effects strengthen with growing suction severity until σ ≈ 6. Above this point, no further changes are observed in the turbulent quantities. The reduction in the size and energy content of the logarithmic layer is responsible for the reduction of the surface pressure fluctuations at mid-frequencies, while the increased energy content in the buffer layer increases the pressure spectral content at high frequencies. The estimates of the far-field trailing edge noise show that flow suction leads to a noise reduction at mid-frequencies with penalties observed at low and high frequencies. Flow suction at an angle of α = 70° and σ ≈ 6 exhibits the best performance in reducing the estimated far-field overall noise levels. Above this point, further increasing the flow suction severity does not provide any additional noise reduction benefits.

Tracking the flapping motion of flow separation using pointwise measurement

In recent investigations of the unsteadiness of flow separation, time-resolved whole-field information, such as the temporal variation of reverse flow area and proper orthogonal decomposition modes, is commonly used to quantify the flapping motion of separation bubbles. In the present study, we explore the possibility of tracking the flapping motion of flow separation using only pointwise measurements. A generalized framework for designing the optimal number and positions of measurement points is presented and assessed using time-resolved particle image velocimetry measurement data for turbulent flow separations induced by a broad range of two- and three-dimensional surface-mounted bluff bodies. Two models are proposed to approximate the temporal variation of reverse flow area over the bluff bodies. These two models require only the mean reattachment length, mean velocity at the body height in the oncoming flow, and time-resolved single- or two-point measurements of streamwise velocity. The optimal location for the single-point model is in the rear part of the mean separation bubble around the highest elevation of the mean separating streamline. While the single-point model predicts the temporal variation of reverse flow area reasonably well, it consistently misidentifies the subdominant frequency of reverse flow area as the dominant one. For the two-point model, one measurement point is in the rear part of the mean separation bubble and the other measurement point is slightly downstream of the mean reattachment point. The two-point model reproduces the temporal variation as well as the dominant frequency of reverse flow area remarkably well. Overall, the present study proposes a simple and reliable method to track the temporal variation of reverse flow area and holds promise for the future development of active closed-loop flow control based on real-time flapping motion of separation bubbles.

Incoming flow measurements of a utility-scale wind turbine using super-large-scale particle image velocimetry

We present incoming flow characterization of a 2.5 ​MW turbine at high spatio-temporal resolution, using super-large-scale particle image velocimetry (SLPIV). The datasets have a field of view of 85 ​m (vertical) × 40 ​m (streamwise) centered at 0.2 rotor diameter upstream. The mean field shows the presence of the induction zone and a distinct region with enhanced vertical velocity. In comparison to vortex theory, SLPIV streamwise velocity presents a steeper velocity drop close to the rotor plane and a more confined induction zone. Time series of nacelle sonic anemometer and SLPIV measured streamwise velocity outside the induction zone show generally matched trends with time-varying discrepancies due to the induction and nacelle effects. The discrepancy, characterized by the sonic-SLPIV velocity ratio, is normally distributed and is less than unity 85% of the time. Data shows both yaw error and incident angle have direct impacts on this ratio, while the intensity of short-term velocity fluctuation has limited effect. Increased yaw error leads to an increase in both the mean and the spread of the ratio. The ratio decreases when the incident angle changes from pointing downward to zero. Further change from zero to pointing upward causes it to plateau with its fluctuations augmented.

Spatial averaging effects on the streamwise and wall-normal velocity measurements in a wall-bounded turbulence using a cross-wire probe

The spatial averaging effects due to a cross-wire probe on the measured turbulence statistics in a wall-bounded flow are investigated using a combined approach of direct numerical simulation data, theoretical methods and experiments. In particular, the wire length (l), spacing () and angle () of a cross-wire probe configured to measure the streamwise and wall-normal velocities are systematically varied to isolate effects of each parameter. The measured streamwise velocity from a cross-wire probe is found to be an average of the filtered velocities sensed by the two wires. Thus, in general, an increase in the sensor dimensions when normalised by viscous units leads to an attenuated variance for the streamwise velocity (), resulting from a larger contribution to the spatial averaging process from poorly correlated velocities. In contrast, the variance for the wall-normal velocity () can be amplified, and this is shown to be the result of an additional contributing term (compared to ) due to differences in the filtered wire-normal velocity between the two wires. This additional term leads to a spurious wall-normal velocity signal, resulting in an amplified variance recorded by the cross-wire probe. Compared to the streamwise and wall-normal velocity variances, the Reynolds shear stress () perhaps surprisingly shows less variation when l, and are varied. The robustness of Reynolds shear stress to the finite sensor size is due to two effects: (i) Reynolds shear stress is devoid of energetic contributions from the near-isotropic fine scales unlike the and statistics, hence cross-wire probe dimensions are typically sufficiently small in terms of viscous unit to adequately capture the statistics for a range of l and investigated; (ii) the dependency arises due to cross terms between the filtered velocities from two wires, however, it turns out that these terms cancel one another in the case of Reynolds shear stress, but not for the and statistics. We note that this does not, however, suggest that is easier to measure accurately than the normal stresses; on the contrary, in a companion paper (Baidya et al 2019 Meas. Sci. Technol. 30 085301) we show that measurements are more prone to errors due to uncertainty in probe geometry and calibration procedure.

Minimizing recalibration using a non-linear regression technique for thermal anemometry

A new method to minimize recalibration in thermal anemometry using a non-linear regression technique is investigated. This method finds potential applications in cases of correcting for non-thermal calibration drifts in long measurements and scenarios where direct calibration of the hot films/hot wires is not possible or suffers significant uncertainties. The essential input for this technique is the a priori knowledge of the first three or four moments of velocity or wall-shear stress for a given Reynolds number. These can be obtained from a separate database (experimental or numerical) in cases where this technique is used as an alternative to direct calibration, or from a previous or simultaneous set of experiments when correcting for non-thermal calibration drifts. Using this input, the coefficients for the assumed calibration functional form can be obtained by an error minimization process. Illustrative results are shown for channel flows where glue-on hot-film probes and hot-wire probes are used for wall-shear stress and streamwise velocity measurements, respectively. There is found to be a good agreement between the velocity and wall-shear stress obtained using regression and prior calibration, which is confirmed using both time history and probability density function plots. Sensitivity to the form of calibration relationship, number of moments, and number of samples required for the regression are conducted. Through examples, it is observed that this method works well in estimating the data when moments obtained from a numerical database are used and also works well in correcting for non-thermal calibration drifts. This technique is also shown to work well for the estimation of data from the voltage signals if moments are available for a Reynolds number “close” to, but not the same as, the measured Reynolds number. One additional potential scenario for application related to the measurement in external flows is then discussed.Graphic abstract

Thermal diffusion interface inside a horizontal pipe flow compared between laminar and turbulent flow regimes

A visualization of thermal diffusion in a horizontal pipe flow is conducted to elucidate the axial diffusion characteristics of two fluids of differing temperatures, particularly those flows between the laminar and turbulent flow regimes. Tracer particles are used to detect the thermal diffusion interface as well as to measure streamwise velocity profiles. We found that the Hagen–Poiseuille parabolic velocity profile established a long axial diffusion length that drives thermal convection in the pipe cross-sectional plane. This situation results in a 3D interface at Reynolds number, Re = 600, and a vertically stratified interface at Re = 1900. In turbulent flows at Re = 5700, an anti-diffusion spot appears in the front section before undergoing rapid mixing under turbulence. From the visualized particle images, the apparent axial coefficients of diffusion were measured and compared with the friction properties of the pipe. Furthermore, particle image velocimetry (PIV) explored the two-way coupling mechanism of between the temperature and the velocity within the thermal diffusion process.

Design and validation of a nanoscale cross-wire probe (X-NSTAP)

A nano-sized crossed thermal anemometer (X-NSTAP) was developed and validated for measurements of two-components of velocity at high Reynolds numbers. The new sensor design is based on the single-component nanoscale thermal anemometry probe (NSTAP) previously used to acquire streamwise velocity measurements at high Reynolds numbers. The new sensor can, simultaneously, measure two components of velocity with a spatial resolution of $$42\times 42\times 50 \, \upmu {\text {m}}$$ , an order of magnitude smaller in each dimension than conventional cross-wires. The new X-NSTAP design features several structural and manufacturing modifications to improve the aerodynamic performance of the sensor compared to previous nanoscale cross-wire designs. The effects of different manufacturing modifications were evaluated using dye visualizations over scale models of the sensor tip. The pitch sensitivity of the final sensor design was evaluated in an open-loop wind-tunnel and was comparable to the single-component NSTAP design. The X-NSTAP was then deployed in the Princeton Superpipe to acquire axial and radial velocity measurements up to friction Reynolds numbers, $$Re_\tau = 24{,}000$$ with good agreement to existing studies.

On the relevance of Reynolds stresses in resolvent analyses of turbulent wall-bounded flows

The ability of linear stochastic response analysis to estimate coherent motions is investigated in turbulent channel flow at the friction Reynolds number $\text{Re}_{\unicode[STIX]{x1D70F}}=1007$. The analysis is performed for spatial scales characteristic of buffer-layer and large-scale motions by separating the contributions of different temporal frequencies. Good agreement between the measured spatio-temporal power spectral densities and those estimated by means of the resolvent is found when the effect of turbulent Reynolds stresses, modelled with an eddy-viscosity associated with the turbulent mean flow, is included in the resolvent operator. The agreement is further improved when the flat forcing power spectrum (white noise) is replaced with a power spectrum matching the measures. Such a good agreement is not observed when the eddy-viscosity terms are not included in the resolvent operator. In this case, the estimation based on the resolvent is unable to select the right peak frequency and wall-normal location of buffer-layer motions. Similar results are found when comparing truncated expansions of measured streamwise velocity power spectral densities based on a spectral proper orthogonal decomposition to those obtained with optimal resolvent modes.

Local transport of passive scalar released from a point source in a turbulent boundary layer

Simultaneous measurements of streamwise velocity ($\tilde{U}$) and concentration ($\tilde{C}$) for a horizontal plume released at eight different vertical locations within a turbulent boundary layer are discussed in this paper. These are supplemented by limited simultaneous three-component velocity and concentration measurements. Results of the integral time scale ($\unicode[STIX]{x1D70F}_{c}$) of concentration fluctuations across the width of the plume are presented here for the first time. It is found that$\unicode[STIX]{x1D70F}_{c}$has two distinct peaks: one closer to the plume centreline and the other at a vertical distance of plume half-width above the centreline. The time-averaged streamwise concentration flux is found to be positive and negative, respectively, below and above the plume centreline. This behaviour is a resultant of wall-normal velocity fluctuations ($w$) and Reynolds shear stress ($\overline{uw}$). Confirmation of these observations is found in the results of joint probability density functions of$u$(streamwise velocity fluctuations) and$\tilde{C}$as well as that of$w$and$\tilde{C}$. Results of cross-correlation coefficient show that high- and low-momentum regions have a distinctive role in the transport of passive scalar. Above the plume centreline, low-speed structures have a lead over the meandering plume, while high-momentum regions are seen to lag behind the plume below its centreline. Further examination of the phase relationship between time-varying$u$and$c$(concentration fluctuations) via cross-spectrum analysis is consistent with this observation. Based on these observations, a phenomenological model is presented for the relative arrangement of a passive scalar plume with respect to large-scale velocity structures in the flow.

Uma comparação dos erros de estimativa da taxa de dissipação de energia cinética da turbulência por diferentes métodos na camada-limite atmosférica

The dissipation rate of the turbulence kinetic energy (") in the atmosphere can be indirectly obtained from high-frequency measurements of streamwise wind velocity, when using the inertial subrange theory predicted by Kolmogorov for the spectrum, second order structure function or ogive. To estimate the error intrinsic to these estimations, a series of synthetic spectra was constructed from the theoretical spectrum combined with random rrors, which were then used to obtain structure functions and ogive. The " estimation from spectra or structure functions presented a root mean square value of approximately 2% of the expected value of ", whereas the estimation from ogives had errors of approximately 1:3%. A correction factor is needed in the estimations using the ogive and the structure function in order to remove the bias caused by the finite Nyquest frequency. Due tothe smaller error, the ogive provides the best approach for indirect estimation of " in the atmospheric boundary layer.

Retrospective cost adaptive Reynolds-averaged Navier–Stokes k–ω model for data-driven unsteady turbulent simulations

This paper presents a data-driven computational model for simulating unsteady turbulent flows, where sparse measurement data is available. The model uses the retrospective cost adaptation (RCA) algorithm to automatically adjust the closure coefficients of the Reynolds-averaged Navier–Stokes (RANS) k–ω turbulence equations to improve agreement between the simulated flow and the measurements. The RCA-RANS k–ω model is verified for steady flow using a pipe-flow test case and for unsteady flow using a surface-mounted-cube test case. Measurements used for adaptation of the verification cases are obtained from baseline simulations with known closure coefficients. These verification test cases demonstrate that the RCA-RANS k–ω model can successfully adapt the closure coefficients to improve agreement between the simulated flow field and a set of sparse flow-field measurements. Furthermore, the RCA-RANS k–ω model improves agreement between the simulated flow and the baseline flow at locations at which measurements do not exist. The RCA-RANS k–ω model is also validated with experimental data from 2 test cases: steady pipe flow, and unsteady flow past a square cylinder. In both test cases, the adaptation improves agreement with experimental data in comparison to the results from a non-adaptive RANS k–ω model that uses the standard values of the k–ω closure coefficients. For the steady pipe flow, adaptation is driven by mean stream-wise velocity measurements at 24 locations along the pipe radius. The RCA-RANS k–ω model reduces the average velocity error at these locations by over 35%. For the unsteady flow over a square cylinder, adaptation is driven by time-varying surface pressure measurements at 2 locations on the square cylinder. The RCA-RANS k–ω model reduces the average surface-pressure error at these locations by 88.8%.

Flow field interactions between two tandem cyclists

Aerodynamic drag is the primary resistive force acting on cyclists at racing speeds. Many events involve cyclists travelling in very close proximity. Previous studies have shown that interactions result in significant drag reductions for inline cyclists. However, the interaction between cyclist leg position (pedalling) and the vortical flow structures that contribute significantly to the drag on an isolated cyclist has not previously been quantified or described for tandem cyclists of varying separation. To this end, scale model cyclists were constructed for testing in a water channel for inline tandem configurations. Particle image velocimetry was used to capture time-averaged velocity fields around two tandem cyclists. Perhaps surprisingly, the wake of a trailing cyclist maintains strong similarity to the characteristic wake of a single cyclist despite a significant disturbance to the upstream flow. Together with streamwise velocity measurements through the wake and upstream of the trailing cyclist, this work supports previous findings, which showed that the trailing cyclist drag reduction is primarily due to upstream sheltering effects reducing the stagnation pressure on forward-facing surfaces.

Evolution of zero-pressure-gradient boundary layers from different tripping conditions

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.

Properties of the streamwise velocity fluctuations in the inertial layer of turbulent boundary layers and their connection to self-similar mean dynamics

Well-resolved streamwise velocity measurements are used to investigate three measures of self-similarity in the spatial inertial sublayer of turbulent boundary layers. The emergence of self-similarity in the inertial sublayer requires a high Reynolds number, and thus a relatively wide range of δ+=δuτ/ν(1400≲δ+≲20,000) is explored. The measures investigated include the Kullback–Leibler divergence (KLD) used in turbulent flow analysis by Tsuji et al. (2005), the logarithmic decrease of the even statistical moments studied by Meneveau and Marusic (2013), and the diagnostic plot of Alfredsson and Örlü (2010). These measures are compared with the analyses of Fife et al. (2005) that determine and exploit an invariant form of the mean momentum equation. A primary focus is on domain(s) where the self-similar behaviors are analytically predicted and empirically observed. The present findings indicate that the approximately constant KLD and approximately logarithmic moment profiles reside in a region that is interior to the bounds of the self-similar inertial domain associated with the mean momentum equation. Conversely, the bounds of the self-similar region on the diagnostic plot correspond closely to the theoretically estimated bounds. Results are briefly discussed relative to Townsend’s notion of outer layer similarity, and, on the inertial domain, the physical existence of uniform momentum zones segregated by narrow vortical fissures.

Improvement of the Lateral Distribution Method based on the mixing layer theory

The accurate prediction of depth-averaged streamwise velocity, boundary shear stress and lateral shear stress are important requisites for the estimation of the flow depth associated with flood events in compound river channels composed of main channel and floodplain. This engineering problem may be tackled through the analytical solution of the depth-averaged momentum equation. Under uniform flow, this solution relies on the calibration of three descriptors of the bottom friction, secondary currents and lateral shear stress. In this paper, the analytical solution materialized in the Lateral Distribution Method is revisited through the consideration of a new panel division. Accurate measurements of streamwise and spanwise velocities as well as of boundary shear stress are used to obtain new predictors of the coefficients describing the effects of bottom friction, secondary currents and lateral shear.The new lateral division of the compound channel into four panels is physically based on the mixing layer width, which is computed by an iterative procedure easily implemented in practical applications.

Spatial averaging of streamwise and spanwise velocity measurements in wall-bounded turbulence using ∨- and ×-probes

The effect of finite dimensions of ∨- and ×-probes is investigated for the measurement of mean and variances of streamwise and spanwise velocities in wall-turbulence. The probes are numerically simulated using a Direct Numerical Simulation database of channel flow at a friction Reynolds number (Reτ) of 934 by varying the probe parameters, namely, the wire-lengths (l), the angle between the wires (θ) and the spacing between the wires (Δs). A single inclined wire is first studied to isolate the effect of l and θ. Analytical expressions for the variances of the streamwise and spanwise velocities are derived by applying a linear-box-type filter to the unfiltered velocity field for both ∨- and ×-probes (at θ = 45°, and arbitrary l and Δs). A similar expression for the streamwise variance in the case of a single inclined wire (for arbitrary l and θ) is also derived. These analytical expressions, supplemented with a model for the correlation over the wire-length, compare favourably with the numerical simulation results, and more importantly explain various trends that are observed in the variances with varying parameters. Close to the wall (where the errors are generally higher) the errors in spanwise variances of the ×-probes are much lower than the ∨-probes, owing to an ‘error-cancelling’ mechanism present in ×-probes due to the effect of l and Δs, as well as due to the procedure of recovering the velocities from two wires. The errors in the streamwise variances are comparable for both ∨- and ×-probes. On the other hand, mean velocities are measured with almost no error by the ∨-probe, whereas the ×-probe induces finite errors in mean velocities due to the fact that the two wires experience different mean velocities in ×-probes unlike ∨-probes. These results are explained using the corresponding analytical results, which also show that under the effect of a linear filter, measured variances depend only on the fluctuating velocities (more precisely on the two-point correlations) and the measured means depend only on the unfiltered mean. The various results are found to be in accordance with the experimental measurements carried out in a turbulent boundary layer at Reτ ≈ 5000. Finally, considering the physical positioning of wires in the ∨- and ×-probes combined with the above results suggests that ×-probes might be more suitable for stream–spanwise velocity measurements than the ∨-probes in conventional wind tunnels.

A generalized log law formulation for a wide range of boundary roughness typically encountered in natural streams

AbstractApplying fluid mechanics principles to mobile bed conditions is simplified by demonstrating that fitting log profiles to streamwise velocity measurements using the plane of zero velocity is applicable to a larger range of roughness conditions than previously expected. Four sets of detailed velocity measurements obtained under the supervision of the authors were analyzed encompassing sediment‐scale roughness elements, roughness caused by rigid vegetation, and large‐scale roughness elements comprised of mobile bed forms. The analyses resulted in similar normalized zero‐plane displacements for all roughness types considered. The zero‐plane displacements, dh, normalized by roughness height, ks, were 0.20 and 0.26 for the sediment‐ and vegetation‐scale experiments, respectively. The results for two experiments with bed form dominated roughness were 0.41 and 0.34. Estimates of dh/ks ranging from 0.2 to 0.4 are therefore recommended for a range of roughness types with the higher end of the range more appropriate for the larger, bed form‐scale roughness elements, and the lower end for the sediment‐scale roughness elements. In addition, it is demonstrated that the location of the plane of zero velocity is temporally constant even when the bed height is not. The findings can be applied to field velocity measurements under mobile bed conditions facilitating the calculation of turbulence parameters such as shear velocity by using point measurements and providing guidelines for the estimation of an appropriate value for zero‐plane displacement.