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.

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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.

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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.

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We carry out direct numerical simulations of turbulent flow over riblets, streamwise- aligned grooves that are designed to reduce drag by modifying the near-wall flow. Twenty riblet geometries and sizes are considered, namely symmetric triangular with tip angle, and, asymmetric triangular, blade and trapezoidal. To save on computational cost, simulations are performed using the minimal-channel flow configuration. With this unprecedented breadth of high-fidelity flow data near the wall, we are able to obtain more general insights into the flow physics of riblets. As observed by García-Mayoral & Jiménez (J. Fluid Mech., vol. 678, 2011, pp. 317-347), we confirm that the drag-change curves of all the present groove geometries better collapse when reported with the viscous-scaled square root of the groove area, rather than the riblet spacing. Using a two-dimensional generalization of the Fukagata-Iwamoto-Kasagi identity in difference form we isolate the different drag-change contributions. We show that the drag increase associated with dispersive stresses carried by secondary flows can be as important as the one associated with the turbulent stresses and the pre-eminence of dispersive stresses can be estimated by the groove width at the riblet mean height.@en

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.

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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.

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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.

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