The measurements by Zagarola & Smits (1998) of mean velocity profiles in fully developed turbulent pipe flow are repeated using a smaller Pitot probe to reduce the uncertainties due to velocity gradient corrections. A new static pressure correction (McKeon & Smits 2002) is used in analysing all data and leads to significant differences from the Zagarola & Smits conclusions. The results confirm the presence of a power-law region near the wall and, for Reynolds numbers greater than $230\,{\times}\,10^3$ ($R^+\,{>}\,5\,{\times}\,10^3$), a logarithmic region further out, but the limits of these regions and some of the constants differ from those reported by Zagarola & Smits. In particular, the log law is found for $600\,{<}\, y^+\,{<}\,0.12R^+$ (instead of $600\,{<}\,y^+\,{<}\,0.07R^+$), and the von Kármán constant $\kappa$, the additive constant $B$ for the log law using inner flow scaling, and the additive constant $B^*$ for the log law using outer scaling are found to be $0.421 \pm 0.002$, $5.60 \pm 0.08 $ and $1.20 \pm 0.10$, respectively, with 95% confidence level (compared with $0.436 \pm 0.002$, $6.15 \pm 0.08$, and $1.51 \pm 0.03$ found by Zagarola & Smits). The data also confirm that the pipe flow data for Re$_D\,{\le}\,13.6\,{\times}\,10^6$ (as a minimum) are not affected by surface roughness.

Statistics of the streamwise velocity component in fully developed pipe flow are examined for Reynolds numbers in the range $5.5 \times 10^4 \le \hbox{\it Re}_D \le 5.7 \times 10^6$. Probability density functions and their moments (up to sixth order) are presented and their scaling with Reynolds number is assessed. The second moment exhibits two maxima: the one in the viscous sublayer is Reynolds-number dependent while the other, near the lower edge of the log region, follows approximately the peak in Reynolds shear stress. Its locus has an approximate $(R^+)^{0.5}$ dependence. This peak shows no sign of ‘saturation’, increasing indefinitely with Reynolds number. Scalings of the moments with wall friction velocity and $(U_{cl}-\overline{U})$ are examined and the latter is shown to be a better velocity scale for the outer region, $y/R > 0.35$, but in two distinct Reynolds-number ranges, one when $\hbox{\it Re}_D < 6 \times 10^4$, the other when $\hbox{\it Re}_D > 7 \times 10^4$. Probability density functions do not show any universal behaviour, their higher moments showing small variations with distance from the wall outside the viscous sublayer. They are most nearly Gaussian in the overlap region. Their departures from Gaussian are assessed by examining the behaviour of the higher moments as functions of the lower ones. Spectra and the second moment are compared with empirical and theoretical scaling laws and some anomalies are apparent. In particular, even at the highest Reynolds number, the spectrum does not show a self-similar range of wavenumbers in which the spectral density is proportional to the inverse streamwise wavenumber. Thus such a range does not attract any special significance and does not involve a universal constant.

The coherent structures of a turbulent wake generated behind a bluff three-dimensional axisymmetric body are investigated experimentally at a diameter-based Reynolds number of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\sim }2\times 10^5$ . Proper orthogonal decomposition of base pressure measurements indicates that the most energetic coherent structures retain the structure of the symmetry-breaking laminar instabilities and are manifested as unsteady vortex shedding with azimuthal wavenumber $m={\pm }1$ . In a rotating reference frame, the shedding preserves the reflectional symmetry and is linked with a reflectionally symmetric mean pressure distribution on the base. Due to a slow rotation of the symmetry plane of the turbulent wake around the axis of the body, statistical axisymmetry is recovered in the time average. The ratio of the time scales associated with the slow rotation of the symmetry plane and the vortex shedding is of order 100.

A specific feature of three-dimensional bluff body wakes, flow bistability, is a subject of particular recent interest. This feature consists of a random flipping of the wake between two asymmetric configurations and is believed to contribute to the pressure drag of many bluff bodies. In this study we apply the modelling approach recently suggested for axisymmetric bodies by Rigaset al.(J. Fluid Mech., vol. 778, 2015, R2) to the reflectional symmetry-breaking modes of a rectilinear bluff body wake. We demonstrate the validity of the model and its Reynolds number independence through time-resolved base pressure measurements of the natural wake. Further, oscillating flaps are used to investigate the dynamics and time scales of the instability associated with the flipping process, demonstrating that they are largely independent of Reynolds number. The modelling approach is then used to design a feedback controller that uses the flaps to suppress the symmetry-breaking modes. The controller is successful, leading to a suppression of the bistability of the wake, with concomitant reductions in both lateral and streamwise forces. Importantly, the controller is found to be efficient, the actuator requiring only 24 % of the aerodynamic power saving. The controller therefore provides a key demonstration of efficient feedback control used to reduce the drag of a high-Reynolds-number three-dimensional bluff body. Furthermore, the results suggest that suppression of large-scale structures is a fundamentally efficient approach for bluff body drag reduction.

A modelling methodology to reproduce the experimental measurements of a turbulent flow in the presence of symmetry is presented. The flow is a three-dimensional wake generated by an axisymmetric body. We show that the dynamics of the turbulent wake flow can be assimilated by a nonlinear two-dimensional Langevin equation, the deterministic part of which accounts for the broken symmetries that occur in the laminar and transitional regimes at low Reynolds numbers and the stochastic part of which accounts for the turbulent fluctuations. Comparison between theoretical and experimental results allows the extraction of the model parameters.