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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 Kwonet 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.

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 Baarset 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.

Time-resolved planar particle image velocimetry was used to analyse the structuring of a turbulent boundary layer into uniform momentum zones (UMZs). The instantaneous peak-detection method employed by Adrian et al. (J. Fluid Mech., vol. 422, 2000, pp. 1–54) and de Silva et al. (J. Fluid Mech., vol. 786, 2016, pp. 309–331) is extended to account for temporal coherence of UMZs. The resulting number of zones detected appears to follow a normal distribution at any given instant. However, the extreme cases in which the number of zones is either very high or very low, are shown to be linked with two distinct flow states. A higher than average number of zones is associated with a large-scale $Q2$ event in the log region which creates increased small-scale activity within that region. Conversely, a low number of zones corresponds to a large-scale $Q4$ event in the log region and decreased turbulent activity away from the wall. The residence times, within the measurement plane, of zones belonging to the latter scenario are shown to be on average four times larger than those of zones present during higher than average zone structuring states. For both cases, greater residence times are observed for zones of higher momentum that are generally closer to the free stream.

The turbulence produced by two regular square mesh grids is compared to that produced by a square-fractal-element grid composed of an array of small square fractals. All three grids have approximately the same blockage. One of the regular grids is designed to have the same mesh length, M, as the fractal element grid, while the other matches the maximum bar thickness of the fractal. The transition of the turbulence from a non-equilibrium to a near equilibrium regime is assessed through the scale-by-scale kinetic energy budget and the velocity derivative skewness. It is found that the turbulence produced by all three grids agrees with many of the predictions for equilibrium phenomenology after approximately 20 M, with the regular grids reaching quasi-equilibrium earlier than the fractal. In the far-field, the fractal grid produces comparable or lower \(Re_\lambda \) than the regular grids in both dimensional and non-dimensional measurements of the streamwise position. This is attributed to an extended rapidly decaying non-equilibrium region in the wake of the fractal grid relative to the regular grids.

The effect of numerical differentiation is investigated in the context of evaluating fluctuating velocity and scalar quantities in turbulent flows. In particular, 2-point forward-difference and 3-, 5-, 7-, and 9-point centred-difference schemes are investigated. The spectral technique introduced by Wyngaard (in J Sci Instr 1(2):1105–1108, 1968) for homogeneous turbulence is used to quantify the effects of the schemes. Numerical differentiation is shown to attenuate gradient spectra over a range of wavenumbers. The spectral attenuation, which varies with the order of the scheme, results in a reduction in the measured mean-squared gradients. High-order schemes (e.g. 7- or 9-point) are shown to significantly decrease the attenuation at all wavenumbers and as a result produce more accurate gradients. Hot-wire measurements and direct numerical simulations of decaying homogeneous, isotropic turbulence are found to be in good agreement with the predictions of the analysis, which suggests that high-order schemes can be used to improve empirical gradient estimates. The shape of the probability density functions is also found to be sensitive to the choice of numerical differentiation scheme. The effect of numerical differentiation is also discussed with respect to particle image velocimetry (PIV) measurements of a nominally two-dimensional planar mixing layer. It is found that the relatively low signal-to-noise ratio inherent in typical PIV measurements necessitates the use of low-order schemes to prevent excessive noise amplification, which increases with the order of the scheme. The results of the present work demonstrate that high-order numerical differentiation schemes can be employed to more accurately resolve gradients measured at a given resolution provided the measurements have an adequate signal-to-noise ratio.

A quantification metric is provided to determine the degree to which a particle image velocimetry data set is pixel-locked. The metric is calculated by integrating the histogram equalization transfer function and normalizing by the worst-case scenario to return the percentage pixel-locked. When this metric is calculated for each position in the vector field, it is shown that pixel-locking is non-uniform across the field. Hence, pixel-locking adjustments should be made on a vector-by-vector basis rather than uniformly across a field, although the latter is the common practice. A methodology is provided to compensate for the effects of pixel-locking on a vector-by-vector basis. This includes applying a Gaussian filter directly to the images, processing the images with window deformation, ensuring the vector fields are in pixel displacements, applying histogram equalization calculated at each vector coordinate, and mapping the adjusted vector fields to physical space.

The most expansive active grid parametric study to date is conducted in order to ascertain the relative importance of the various grid parameters. It is identified that the three most important parameters are the Rossby number, Ro, the grid Reynolds number, $$Re_M,$$ and the wing geometry. For $$Ro > 50$$ , an asymptotic state in turbulence intensity is reached where increasing Ro further does not change the turbulence intensity, while other parameters continue to vary. Three wing geometries are used: solid square wings, solid circular wings, and square wings with holes. It is shown that the wings with the greatest blockage produce the highest turbulence intensities and $$Re_\lambda$$ , but that parameters such as the Kolmogorov, Taylor, and integral scales are not significantly influenced by wing geometry. Finally, it is demonstrated that for several different sets of initial conditions that produce the same $$Re_\lambda$$ , the spectra are collapsed everywhere but at the largest scales when normalized by Kolmogorov variables. This result suggests that regardless of the very different origins of the turbulence, the shape of the spectra at high wavenumbers is dependent only on $$Re_\lambda$$ , hence demonstrating a degree of independence from the initial conditions.

A novel square-fractal-element grid was designed in order to increase the downstream measurement range of fractal grid experiments relative to the largest element of the grid. The grid consists of a series of square fractal elements mounted to a background mesh with spacing$L_0 = 100\, {\rm mm}$. Measurements were performed in the region$3.5 \le x/L_0 \le 48.5$, which represents a significant extension to the$x/L_0 < 20$of previously reported square fractal grid measurements. For the region$x/L_0 \gtrsim 24$it was found that a power-law decay region following$\langle {q}^2 \rangle \sim (x - x_0)^m$exists with decay exponents of$m = -1.39$and$-1.37$at$\mathit{Re}_{L_0} = 57\, 000$and$65\, 000$, respectively. This agrees with decay values previously measured for regular grids ($-1 \gtrsim m \gtrsim -1.4$). The turbulence in the near-grid region,$x/L_0 < 20$, is shown to be inhomogeneous and anisotropic, in apparent contrast with previous fractal grid measurements. Nonetheless, power-law fits to the decay of turbulent kinetic energy in this region result in$m = -2.79$, similar to$m \approx -2.5$recently reported by Valente & Vassilicos (J. Fluid Mech., vol. 687, 2011, pp. 300–340) for space-filling square fractals. It was also found that$C_\epsilon $is approximately constant for$x/L_0 \ge 25$, while it grows rapidly for$x/L_0 < 20$. These results reconcile previous fractal-generated turbulence measurements with classical grid turbulence measurements.