The spatial response of a turbulent boundary layer subjected to a streamwiseperiodic square-wave (SqW) variation of the spanwise wall velocity is investigated experimentally. The SqW forcing is implemented via a setup comprising 48 spanwise-running belts, which is used to assess the influence of the (viscous-scaled) forcing wavelength for: sub-optimal ?⁺_x = 471, near-optimum ?⁺_x = 942, and post-optimal ?⁺_x = 1884 conditions, at a fixed spanwise-velocity amplitude A+ = 12. Previous studies have identified a high phase-wise rate-of-change of the Stokes strain (wall-normal gradient of spanwise velocity) - the Stokes-strain rate (SSR) - to drive the attenuation of turbulence, whereas recovery of turbulence was found when SSR ~ 0 extended over a sufficient fetch of the phase, referred to as subphases I and II, respectively. For the SqW, subphase-I occurs over a fixed short fetch where the sign of wall velocity reverses, whereas subphase-II extends over the rest of the half-phase, where the wall velocity remains constant. These SSRrelated hypotheses are confirmed; the phase-wise variation of turbulence attenuation and recovery, however, is established only for the post-optimal case, owing to its extended fetch of subphase-II. An out-of-phase trend between C_f and the turbulence is elucidated by evaluating the internal boundary layer (IBL) thickness d_i, where C_fand d_ishow a clear correlation.

A surface geometry consisting of parallel, meandering streamwise grooves has been experimentally studied as an alternative means of passive transverse forcing of turbulent boundary-layer flow. Particle image velocimetry (PIV) was the main diagnostic tool for characterising the properties of the induced spanwise flow. Contrary to the original expectation, the flow does not exhibit a spanwise-uniform undulation aligned with the grooves; instead, a converging-diverging flow pattern results. This flow pattern can be attributed to the spanwise periodicity of the lateral pressure gradient. The forcing effect is found to initially increase with the groove amplitude, but it saturates when the groove slope becomes too steep. The observed induced flow, referred to as a Passive Stokes Layer (PSL), can be considered as being composed of an inertial (pressure-driven) outer solution generated by the displacement effect of the non-smooth surface geometry, and a viscous inner solution to accommodate the no-slip condition at the wall. The mechanism of transverse flow generation is elucidated by an inviscid flow model that relates the forcing to the surface geometric properties, with predictions that are in good agreement with the experimental results. Although a reduction in the near-wall turbulence levels over the groove surfaces is observed, no direct evidence for drag reduction is apparent in the mean-flow data. Instead, an estimate of the frictional drag potential is based on establishing a tentative relation to an equivalent spatial Stokes layer (SSL) induced by active wall forcing. This theoretical comparison indicates that the induced passive forcing is sufficient to act on the (active) spanwise forcing mechanism, but produces at most a few per cent of frictional drag reduction. Any potential savings are likely offset by pressure drag and other losses, so that, similar to active forcing, its potential for net drag reduction in practical applications is limited.

Turbulent boundary layers characterised by friction Reynolds numbers in the range (Formula presented) and flowing over flush-mounted passively rotating discs are investigated in a wind tunnel with the purpose of reducing the skin-friction drag. The test surface is composed of thirty-two rotating discs arranged in a staggered configuration and supported by bearings mounted in cylindrical cavities. As the discs are half-covered by thin rigid plates, a steady rotation of the discs is sustained via the asymmetric distribution of the wall-shear stress exerted by the wall turbulence on the exposed halves of the discs. Direct force measurements reveal that the drag increases with respect to a flat-plate case because of the flow interaction with the disc housings and the covering plates. The effect of the disc motion is isolated and a 3 % drag reduction is measured with respect to the flow over stationary discs. The skin-friction identity by Elnahhas & Johnson (2022) J. Fluid Mech. 940, extended herein to include the disc-flow effects, is utilised for the first time to analyse experimental data. This direct-slip effect, quantified by using the measured disc angular velocities in the Elnahhas–Johnson identity, is negligible. Measurements obtained by particle image velocimetry disclose that a roughness mean-flow effect occurs between adjacent discs because of the clearance gaps around the discs and that a downwash secondary flow exists near the covering plates, analogous to flows over streamwise-elongated rectangular roughness elements. This downwash velocity is streamwise modulated because of the spanwise disc motion and alters the wall-normal transport term in the Elnahhas–Johnson identity, thus reducing the drag locally. The velocity covariances are enhanced in the proximity of adjacent discs, in line with the roughness effect in that region. The Reynolds-shear-stress term in the Elnahhas–Johnson identity is thereby globally enhanced. Nonetheless, the near-wall one-point and two-point covariances of the velocity fluctuations and the Reynolds shear stresses are reduced in magnitude and spatial coherence. This result is the first experimental evidence confirming that the attenuation of the Reynolds shear stresses is the central drag-reducing mechanism behind the rotating-disc flow.

A new facility for studying turbulent boundary layer flows has been developed at the Delft University of Technology and is referred to as the DU-BLF: Delft University Boundary Layer Facility. Its design and boundary layer data characteristics are presented in the current work. The DU-BLF can be employed for a range of studies revolving around boundary layer flows, e.g., covering fundamentals of boundary layer development, flow control with passive surface modifications, and control efforts with active technologies. A modular setup of the test section allows for a relatively long development length, with both physical and optical access over its complete extent. For the present characterisation, a turbulent boundary layer was developed under a zero (streamwise) pressure gradient, with the aid of a flexible ceiling. We establish the general flow characteristics, including freestream turbulence intensity levels, acoustic noise characteristics, boundary layer-integral parameters, and wall-normal profiles of the first and second-order turbulence statistics. Results are validated by employing multiple measurement techniques, namely, hot wire anemometry, particle image and tracking velocimetry, and wall-pressure measurements. Results are shown for friction Reynolds numbers up to Re _τ≈5100, and reveal that the boundary layer flow adheres to the expected behaviour of canonical wall-bounded turbulence. Data of the current turbulent boundary layer measurements are made available online.

This study investigates the spatial evolution of a zero pressure gradient turbulent boundary layer (TBL) imposed by a square-wave (SqW) of steady spanwise wall-forcing, which varies along the streamwise direction (x). The SqW wall-forcing is imposed experimentally via a series of streamwise periodic belts running in opposite spanwise directions, following the methodology of Knoop et al. [Exp. Fluids 65, 65 (2024)]0723-486410.1007/s00348-024-03799-9, with the streamwise extent increased to beyond ∼11 times the boundary layer thickness (δo) in the present study. This unique setup is leveraged to investigate the influence of viscous-scaled wavelength of SqW wall-forcing on the turbulent drag reduction efficacy for λx+=471 (suboptimal), 942 (near-optimal), and 1884 (postoptimal conditions), at fixed viscous-scaled wall-forcing amplitude, A+=12, and friction Reynolds number, Reτ=960. The TBL's response to this wall-forcing is elucidated by drawing inspiration from established knowledge on traditionally studied sinusoidal forcing, based on analysis of the streamwise-phase variation of the Stokes strain rate (SSR). The analysis reveals the SqW forcing to be characterized by a combination of two markedly different SSR regimes whose influence on the overlying turbulence is found to depend on the forcing waveform: subphase I of local and strong impulses of SSR downstream of the half- (λx/2) and full-phase (λx) locations, associated with a reversal in spanwise forcing directions, leading to significant turbulence attenuation, and subphase II of near-zero SSR over the remainder of forcing phase that enables turbulence recovery (when wall-forcing magnitudes and direction remain constant). Upon the initial imposition of the SqW forcing, the Reynolds stresses are strongly attenuated over the short streamwise extent of x/δ0<0.5 for all wavelengths, whereas the skin-friction transient is more gradual. Thereafter, once the forcing is ultimately established, the suboptimum and optimum wavelength regimes display no distinctive responses to the individual SSR subphases; rather, the drag-reduced TBL response is quasi-streamwise homogeneous. In contrast, an SSR-related phenomenology establishes itself clearly for the postoptimal case, in which a local attenuation of near-wall turbulence characterizes subphase I, while the turbulent energy recovers in subphase II owing to the extended region of near-zero SSR.

We present an experimental realisation of spatial spanwise forcing in a turbulent boundary layer flow, aimed at reducing the frictional drag. The forcing is achieved by a series of spanwise running belts, running in alternating spanwise direction, thereby generating a steady spatial square-wave forcing. Stereoscopic particle image velocimetry in the streamwise–wall-normal plane is used to investigate the impact of actuation on the flow in terms of turbulence statistics, drag performance characteristics, and spanwise velocity profiles, for a non-dimensional wavelength of λ_x⁺=397. In line with reported numerical studies, we confirm that a significant flow control effect can be realised with this type of forcing. The scalar fields of the higher-order turbulence statistics show a strong attenuation of stresses and production of turbulence kinetic energy over the first belt already, followed by a more gradual decrease to a steady-state energy response over the second belt. The streamwise velocity in the near-wall region is reduced, indicative of a drag-reduced flow state. The profiles of the higher-order turbulence statistics are attenuated up to a wall-normal height of y⁺≈100, with a maximum streamwise stress reduction of 45% and a reduction of integral turbulence kinetic energy production of 39%, for a non-dimensional actuation amplitude of A⁺=12.7. An extension of the classical laminar Stokes layer theory is introduced, based on the linear superposition of Fourier modes, to describe the non-sinusoidal boundary condition that corresponds to the current case. The experimentally obtained spanwise velocity profiles show good agreement with this extended theoretical model. The drag reduction was estimated from a linear fit in the viscous sublayer in the range 2≤y⁺≤5. The results are found to be in good qualitative agreement with the numerical implementations of Viotti et al. (Phys Fluids 21, 2009), matching the drag reduction trend with A⁺, and reaching a maximum of 20%. Graphical abstract: (Figure presented.)