Accurate predictions of the drag penalty in rough-wall flows require careful characterisation of surface roughness to determine the equivalent sand-grain roughness height (k_s). The procedure involves measuring wall-shear stress (τ_w) using direct or indirect methods and analyzing velocity profiles. However, indirect methods often rely on assumptions whose validity cannot always be guaranteed. In this paper (partly based on the study [1]), wind tunnel measurements on a realistic rough surface scanned from a fouled ship hull are carried out to evaluate drag penalty predictions. Current data enabled the evaluation of k_s and associated wake parameters using several methods, which were then used for full-scale drag penalty predictions at high Reynolds numbers, with results showing the drag penalty could vary by nearly 15% among methods, highlighting the importance of exercising caution when employing such methods.

Full-scale drag penalty predictions of flows over rough walls require surface roughness characterisation from laboratory experiments or numerical simulations. In either approach, it is necessary to determine the so-called equivalent sand-grain roughness height (k_s ). There are several steps involved in determining this aerodynamic roughness lengthscale, but its procedure typically includes a combination of measurement of wall-shear stress (τ_w ) using direct or indirect methods as well as analysis of velocity profiles. Indirect methods usually rely on assumptions made about flow and its scaling including the validity of universal outer-layer similarity. However, the implications of the underlying assumptions involved in full-scale drag prediction are unclear. In this work, we carry out wind tunnel measurements over a realistic rough surface (from a fouled ship-hull) to evaluate the impact of different methods with an emphasis on using the outer-layer similarity hypothesis for full-scale drag predictions. Wall-shear stress is measured using an in-house floating-element drag balance (DB), and velocity profiles are obtained using particle image velocimetry (PIV), allowing the evaluation of k_s , and the associated wake parameters through several methods. The aerodynamic roughness parameters hence obtained are used for full-scale drag penalty calculations. It is observed that the predicted drag penalty can vary by over 15 % among the different methods highlighting the care that should be taken when employing such methods.

We investigate the underlying physics behind the change in amplitude modulation coefficient in noncanonical wall-bounded flows in the framework of the inner-outer interaction model (IOIM) [Baars, Phys. Rev. Fluids 1, 054406 (2016)2469-990X10.1103/PhysRevFluids.1.054406]. The IOIM captures the amplitude modulation effect, and here we focus on extending the model to noncanonical flows. An analytical relationship between the amplitude modulation coefficient and IOIM parameters is derived, which is shown to capture the increasing trend of the amplitude modulation coefficient with an increasing Reynolds number in a smooth-wall dataset. This relationship is then applied to classify and interpret the noncanonical turbulent boundary layer results reported in previous works. We further present the case study of a turbulent boundary layer after a rough-to-smooth change. Both single-probe and two-probe hotwire measurements are performed to acquire streamwise velocity time series in the recovering flow on the downstream smooth wall. An increased coherence between the large-scale motions and the small-scale envelope in the near-wall region is attributed to the stronger footprints of the overenergetic large-scale motions in the outer layer, whereas the near-wall cycle and its amplitude sensitivity to the superposed structures are similar to that of a canonical smooth-wall flow. These results indicate that the rough-wall structures above the internal layer interact with the near-wall cycle in a similar manner as the increasingly energetic structures in a high-Reynolds number smooth-wall boundary layer.

We study the flow above non-optimal riblets, specifically large drag-increasing and two-scale trapezoidal riblets. In order to reach large Reynolds numbers and large scale separation while retaining access to flow details, we employ a combination of boundary-layer hot-wire measurements and direct numerical simulation (DNS) in minimal-span channels. Although the outer Reynolds numbers differ, we observe fair agreement between experiments and DNS at matched viscous-friction-scaled riblet spacings in the overlapping physical and spectral regions, providing confidence that both data sets are valid. We find that hot-wire velocity spectra above very large riblets with are depleted of near-wall energy at scales that are (much) greater than. Large-scale energy likely bypasses the turbulence cascade and is transferred directly to secondary flows of size, which we observe to grow in strength with increasing riblet size. Furthermore, the present very large riblets reduce the von Kármán constant of the spanwise uniform mean velocity in a logarithmic layer and, thus, reduce the accuracy of the roughness-function concept, which we link to the near-wall damping of large flow structures. Half-height riblets in the groove, which we use as a model of imperfectly repeated (spanwise-varying) riblets, impede in-groove turbulence. We show how to scale the drag optimum of imperfectly repeated riblets based on representative measurements of the true geometry by solving inexpensive Poisson equations.

The probability density function (PDF) of the instantaneous streamwise velocity has consistently been used to extract information on the formation of uniform momentum zones (UMZs) in wall-bounded flows. Its temporal evolution has previously revealed patterns associated with the geometry and amplitude of the underlying velocity fluctuations [Laskari and McKeon, J. Fluid Mech. 913, A6 (2021)0022-112010.1017/jfm.2020.1163]. In this paper, we examine the robustness of these patterns in a variety of data sets including experiments and wall-bounded flow models. Experimental data sets spanning a range of Reynolds numbers, with very long temporal and spatial domains, suggest that the rate of the observed temporal variations scales in inner units. The use of a convection velocity, uniform across heights, to transform space into time has a marginal effect on these features. Similarly, negligible effects are observed between internal and external geometries. Synthetic databases generated following the resolvent framework and the attached eddy model are employed to draw comparisons to the experimental databases. Our findings highlight the distinctive strengths of each: The broadband frequency input of the attached eddy model allows for a better statistical description as opposed to a narrow frequency input in the resolvent data sets; instantaneously, however, representative eddies are seen to lack some structural details leading to the observed temporal behavior, which is better replicated by resolvent modes. Overall, given the considerable variety of the input data tested, the agreement between the data sets highlights the robustness of the spatiotemporal characteristics of the examined UMZs. It also underpins the need for their proper inclusion in UMZ modeling from a statistical as well as an instantaneous viewpoint; the current analysis accentuates important performance indicators for both.

A large-scale spanwise and wall-normal array of sonic anemometers in the atmospheric surface layer is used to acquire all three components of instantaneous fluctuating velocity as well as temperature in a range of stability conditions. These data permit investigation of the three-dimensional statistical structure of turbulence structures. Based on a similar dataset, Krug et al. (Boundary-Layer Meteorol., vol. 172, 2019, pp. 199-214) reported a self-similar range of wall-attached turbulence structures under both unstable and near-neutral stability conditions. They considered only a wall-normal array and thus assessed statistical structure in the wall-normal direction, in relation to the streamwise wavelength. The present work extends the view of a self-similar range of turbulence structures, by including the statistical structure in the spanwise direction. Moreover, by analysing the phase shift between synchronized measurements in the spectral domain, it is inferred how a scale-dependent inclination angle in the streamwise/wall-normal plane varies with stability. Results suggest that the self-similar wall-attached structures have similar aspect ratios between streamwise/wall-normal scales and streamwise/spanwise scales such that for both near-neutral and unstable conditions. Under the most unstable conditions, coherent structures with are inclined at angles as high as relative to the solid boundary, while larger scales exhibit inclination angles of approximately. For near-neutral stability conditions, the angle tends towards for all scales. It is noted that in the near-neutral condition, the structure inclination angle and the aspect ratio - and thus the statistical modelling of coherent structures in the atmospheric surface layer - are highly sensitive to the value of the stability parameter.

In this study, we develop an analytical model to predict the turbulent boundary layer downstream of a step-change in the surface roughness where upstream flow conditions are given. We first revisit the classical model of Elliott (Trans. Am. Geophys. Union, vol. 39, 1958, pp. 1048-1054), who modelled the velocity distribution within and above the internal layer with a simple piecewise logarithmic profile, and evolved the velocity profile using the streamwise momentum equation. Elliott's model was originally developed for an atmospheric surface layer, and to make the model applicable to a spatially developing turbulent boundary layer with finite thickness, we propose a number of more physical refinements, including adding a wake function to the velocity profile, considering the growth of the entire boundary layer in the streamwise direction, and using a more realistic shear stress profile in the momentum equation. In particular, we implement the blending model (Li et al., J. Fluid Mech., vol. 923, 2021, p. A18) to account for the deviation of the mean flow within the internal layer from a canonical velocity profile based on the local wall condition. These refinements lead to improved agreement between the prediction and the measurement, especially in the vicinity of the rough-to-smooth change.

This study presents an experimental dataset documenting the evolution of a turbulent boundary layer downstream of a rough-to-smooth surface transition. To investigate the effect of upstream flow conditions, two groups of experiments are conducted. For the Group-Re cases, a nominally constant viscous-scaled equivalent sand grain roughness is maintained on the rough surface, while the friction Reynolds number ranges from 7100 to 21 000. For the Group-ks cases, is maintained while ranges from 111 to 228. The wall-shear stress on the downstream smooth surface is measured directly using oil-film interferometry to redress previously reported uncertainties in the skin-friction coefficient recovery trends. In the early development following the roughness transition, the flow in the internal layer is not in equilibrium with the wall-shear stress. This conflicts with the common practise of modelling the mean velocity profile as two log laws below and above the internal layer height, as first proposed by Elliott (Trans. Am. Geophys. Union, vol. 39, 1958, pp. 1048-1054). As a solution to this, the current data are used to model the recovering mean velocity semi-empirically by blending the corresponding rough-wall and smooth-wall profiles. The over-energised large-scale motions leave a strong footprint in the near-wall region of the energy spectrum, the frequency and magnitude of which exhibit dependence on and, respectively. The energy distribution in near-wall small scales is mostly unaffected by the presence of the outer flow with rough-wall characteristics, which can be used as a surrogate measure to extract the local friction velocity.

Riblets reduce skin-friction drag until their viscous-scaled size becomes large enough for turbulence to approach the wall, leading to the breakdown of drag-reduction. In order to investigate inertial-flow mechanisms that are responsible for the breakdown, we employ the minimal-span channel concept for cost-efficient direct numerical simulation (DNS) of rough-wall flows (MacDonald et al. in J Fluid Mech 816: 5–42, 2017). This allows us to investigate six different riblet shapes and various viscous-scaled sizes for a total of 21 configurations. We verify that the small numerical domains capture all relevant physics by varying the box size and by comparing to reference data from full-span channel flow. Specifically, we find that, close to the wall in the spectral region occupied by drag-increasing Kelvin–Helmholtz rollers (García-Mayoral and Jiménez in J Fluid Mech 678: 317–347, 2011), the energy-difference relative to smooth-wall flow is not affected by the narrow domain, even though these structures have large spanwise extents. This allows us to evaluate the influence of the Kelvin–Helmholtz instability by comparing fluctuations of wall-normal and streamwise velocity, pressure and a passive scalar over riblets of different shapes and viscous-scaled sizes to those over a smooth wall. We observe that triangular riblets with a tip angle α= 30 ^∘ and blades appear to support the instability, whereas triangular riblets with α= 60 ^∘–90 ^∘ and trapezoidal riblets with α= 30 ^∘ show little to no evidence of Kelvin–Helmholtz rollers.

Opposition-control of the energetic cycle of near wall streaks in wall-bounded turbulence, using numerical approaches, has shown promise for drag reduction. For practical implementation, real-time opposition control is only realizable if there is a degree of coherence between the turbulent velocities passing a sensor and the target point within the flow; for practicality, a sensor (and actuator) should be wall-based to avoid parasitic drag. As such, we here inspect the feasibility of real-time control of the near wall cycle, by considering the coherence between a measurable wall-quantity, being the wall-shear stress fluctuations, and the streamwise and wall-normal velocity fluctuations in a turbulent boundary layer. Synchronized spatial and temporal velocity data from two direct numerical simulations and a fine large eddy simulation at Re_τ≈590 and 2000 are employed. This study shows that the spectral energy of the streamwise velocity fluctuations that is stochastically incoherent with wall signals is independent of Reynolds number in the near wall region (up to the viscous-scaled wall-normal height z⁺≈20). Consequently, the streamwise energy-fraction that is stochastically wall-coherent grows with Reynolds number due to the increasing range of energetic large scales. This thus implies that a wall-based control system has the ability to manipulate a larger portion of the total turbulence energy at off-wall locations, at higher Reynolds numbers, while the efficacy of predicting/targeting the small scales of the near wall cycle remains indifferent with varying Reynolds number. Coherence values of 0.55 and 0.4 were found between the streamwise and wall-normal velocity fluctuations at the near wall peak in the energy spectrogram, respectively, and the streamwise fluctuating friction velocity. These coherence values, which are considerably lower than 1 (maximum possible coherence) suggest that a closed-loop drag reduction scheme targeting near wall cycle streaks alone (based on sensed friction velocity fluctuations) will be of limited success in practice.

This paper examines the recovery of the wall-shear stress of a turbulent boundary layer that has undergone a sudden transition from a rough to a smooth surface. Early work of Antonia & Luxton (J. Fluid Mech., vol. 53, 1972, pp. 737-757) questioned the reliability of standard smooth-wall methods for measuring wall-shear stress in such conditions, and subsequent studies show significant disagreement depending on the approach used to determine the wall-shear stress downstream. Here we address this by utilising a collection of experimental databases at that have access to both 'direct' and 'indirect' measures of the wall-shear stress to understand the recovery to equilibrium conditions of the new surface. Our results reveal that the viscous region recovers almost immediately to an equilibrium state with the new wall conditions; however, the buffer region and beyond takes several boundary layer thicknesses before recovering to equilibrium conditions, which is longer than previously thought. A unique direct numerical simulation database of a wall-bounded flow with a rough-to-smooth wall transition is employed to confirm these findings. In doing so, we present evidence that any estimate of the wall-shear stress from the mean velocity profile in the buffer region or further away from the wall tends to underestimate its magnitude in the near vicinity of the rough-to-smooth transition, and this is likely to be partly responsible for the large scatter of recovery lengths to equilibrium conditions reported in the literature. Our results also reveal that smaller energetic scales in the near-wall region recover to an equilibrium state associated with the new wall conditions within one boundary layer thickness downstream of the transition, while larger energetic scales exhibit an over-energised state for several boundary layer thicknesses downstream of the transition. Based on these observations, an alternative approach to estimating the wall-shear stress from the premultiplied energy spectrum is proposed.

The evolution of turbulent boundary layers downstream of a rough-to-smooth transition is investigated at a range of Reynolds numbers. Measurements are performed at friction Reynolds numbers of 4100, 7100, 14000 and 21000 using hotwire anemometry. The wall-shear stress on the smooth surface in each case is measured directly using oil film interferometry. The growth of the internal layer is studied, and a full recovery of all energetic scales in the energy spectrum of the streamwise velocity fluctuations is observed at 80 boundary layer thicknesses downstream of the roughness transition. A comparison of recovery lengths required for various flow statistics (skin-friction coefficient and energy spectrum) is also presented.

The mean wall shear stress, τ¯ _w, is a fundamental variable for characterizing turbulent boundary layers. Ideally, τ¯ _w is measured by a direct means and the use of floating elements has long been proposed. However, previous such devices have proven to be problematic due to low signal-to-noise ratios. In this paper, we present new direct measurements of τ¯ _w where high signal-to-noise ratios are achieved using a new design of a large-scale floating element with a surface area of 3 m (streamwise) × 1 m (spanwise). These dimensions ensure a strong measurement signal, while any error associated with an integral measurement of τ¯ _w is negligible in Melbourne’s large-scale turbulent boundary layer facility. Wall-drag induced by both smooth- and rough-wall zero-pressure-gradient flows are considered. Results for the smooth-wall friction coefficient, C_f≡ τ¯ _w/ q_∞, follow a Coles–Fernholz relation Cf=[1/κln(Reθ)+C]-2 to within 3 % (κ= 0.38 and C= 3.7) for a momentum thickness-based Reynolds number, Re_θ> 15 , 000. The agreement improves for higher Reynolds numbers to <1 % deviation for Re_θ> 38 , 000. This smooth-wall benchmark verification of the experimental apparatus is critical before attempting any rough-wall studies. For a rough-wall configuration with P36 grit sandpaper, measurements were performed for 10 , 500 < Re_θ< 88 , 500 , for which the wall-drag indicates the anticipated trend from the transitionally to the fully rough regime.

Wavelet analysis is employed to examine amplitude and frequency modulations in broadband signals. Of particular interest are the streamwise velocity fluctuations encountered in wall-bounded turbulent flows. Recent studies have shown that an important feature of the near-wall dynamics is the modulation of small scales by large-scale motions. Small- and large-scale components of the velocity time series are constructed by employing a spectral separation scale. Wavelet analysis of the small-scale component decomposes the energy in joint time–frequency space. The concept is to construct a low-dimensional representation of the small-scale time-varying spectrum via two new time series: the instantaneous amplitude of the small-scale energy and the instantaneous frequency. Having the latter in a time-continuous representation allows a more thorough analysis of frequency modulation. By correlating the large-scale velocity with the concurrent small-scale amplitude and frequency realizations, both amplitude and frequency modulations are studied. In addition, conditional averages of the small-scale amplitude and frequency realizations depict unique features of the scale interaction. For both modulation phenomena, the much studied time shifts, associated with peak correlations between the large-scale velocity and small-scale amplitude and frequency traces, are addressed. We confirm that the small-scale amplitude signal leads the large-scale fluctuation close to the wall. It is revealed that the time shift in frequency modulation is smaller than that in amplitude modulation. The current findings are described in the context of a conceptual mechanism of the near-wall modulation phenomena.