Simulations and experiments at low Reynolds numbers have suggested that skin-friction drag generated by turbulent fluid flow over a surface can be decreased by oscillatory motion in the surface, with the amount of drag reduction predicted to decline with increasing Reynolds number. Here, we report direct measurements of substantial drag reduction achieved by using spanwise surface oscillations at high friction Reynolds numbers ($${{{\mathrm{Re}}}_{\tau }}$$ Re τ ) up to 12,800. The drag reduction occurs via two distinct physical pathways. The first pathway, as studied previously, involves actuating the surface at frequencies comparable to those of the small-scale eddies that dominate turbulence near the surface. We show that this strategy leads to drag reduction levels up to 25% at $${{{{{{{{\mathrm{Re}}}}}}}}}_{\tau }$$ Re τ = 6,000, but with a power cost that exceeds any drag-reduction savings. The second pathway is new, and it involves actuation at frequencies comparable to those of the large-scale eddies farther from the surface. This alternate pathway produces drag reduction of 13% at $${{{{{{{{\mathrm{Re}}}}}}}}}_{\tau }$$ Re τ = 12,800. It requires significantly less power and the drag reduction grows with Reynolds number, thereby opening up potential new avenues for reducing fuel consumption by transport vehicles and increasing power generation by wind turbines.

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 $Re_{\unicode[STIX]{x1D70F}}\approx 4100$ 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 ($z^{+}\lesssim 4$) 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.

Direct numerical simulations (DNS) are reported for open-channel flow over streamwise-alternating patches of smooth and fully rough walls. The rough patch is a three-dimensional sinusoidal surface. Owing to the streamwise periodicity, the flow configuration consists of a step change from smooth to rough, and a step change from rough to smooth. The friction Reynolds number varies from 437 over the smooth patch to 704 over the rough patch. Through the fully resolved DNS dataset it is possible to explore many detailed aspects of this flow. Two aspects motivate this work. The first one is the equilibrium assumption that has been widely used in both experiments and computations. However, it is not clear where this assumption is valid. The detailed DNS data reveal a significant departure from equilibrium, in particular over the smooth patch. Over this patch, the mean velocity is recovered up to the beginning of the log layer after a fetch of five times the channel height. However, over the rough patch, the same recovery level is reached after a fetch of two times the channel height. This conclusion is arrived at by assuming that an error of up to 5 % is acceptable and the log layer, classically, starts from 30 wall units above the wall. The second aspect is the reported internal boundary-layer (IBL) growth rates in the literature, which are inconsistent with each other. This is conjectured to be partly caused by the diverse IBL definitions. Five common definitions are applied for the same DNS dataset. The resulting IBL thicknesses are different by 100 %, and their apparent power-law exponents are different by 50 %. The IBL concept, as a layer within which the flow feels the surface underneath, is taken as the basis to search for the proper definition. The definition based on the logarithmic slope of the velocity profile, as proposed by Elliot (Trans. Am. Geophys. Union, vol. 39, 1958, pp. 1048–1054), yields better consistency with this concept based on turbulence characteristics.

We propose a new length scale as a basis for the modelling of subfilter motions in large-eddy simulations (LES) of turbulent flow. Rather than associating the model length scale with the computational grid, we put forward an approximation of the integral length scale to achieve a non-uniform flow coarsening through spatial filtering that reflects the local, instantaneous turbulence activity. Through the introduction of this grid-independent, solution-specific length scale it becomes possible to separate the problem of representing small-scale turbulent motions in a coarsened flow model from that of achieving an accurate numerical resolution of the primary flow scales. The formulation supports the notion of grid-independent LES, in which a prespecified reliability measure is used. We investigate a length-scale definition based on the resolved turbulent kinetic energy (TKE) and its dissipation. The proposed approach, which we call integral length-scale approximation (ILSA) model, is illustrated for turbulent channel flow at high Reynolds numbers and for homogeneous isotropic turbulence (HIT). We employ computational optimization of the model parameter based on various measures of subfilter activity, using the successive inverse polynomial interpolation (SIPI) and establish the efficiency of this route to subfilter modelling.

Well-resolved numerical simulations of turbulent open channel flows are analyzed to evaluate the accuracy of the 2nd order structure function method (SFM) in estimating the rate of dissipation of turbulent kinetic energy within boundary layers. The objective is to assess the variation in the 2/3 Kolmogorov constants due to flow anisotropy with distance from the wall. Comparison of the dissipation calculated directly from the numerical data, with that from the SFM shows that usage of the canonical constants, based on the assumption of local isotropy, can result in considerable error (>50%) in the prediction of dissipation when using the vertical or spanwise velocity components. From the numerically calculated dissipation, optimal Kolmogorov 2/3 constants were obtained and empirical relations, which account for near-wall effects, were proposed. Usage of the optimal constants will improve estimation of the dissipation rate when the SFM is applied to compute dissipation in geophysical boundary-layer flows.