The Reynolds-number dependence of turbulent channel flow over two irregular rough surfaces, based on scans of a graphite and a grit-blasted surface, is studied by direct numerical simulation. The aim is to characterise the changes in the flow in the immediate vicinity of and within the rough surfaces, an area of the flow where it is difficult to obtain experimental measurements. The average roughness heights and spatial correlation of the roughness features of the two surfaces are similar, but the two surfaces have a significant difference in the skewness of their height distributions, with the graphite sample being positively skewed (peak-dominated) and the grit-blasted surface being negatively skewed (valley-dominated). For both cases, numerical simulations were conducted at seven different Reynolds numbers, ranging from Re τ = 90 to Re τ = 720. The positively skewed surface gives rise to higher friction factors than the negatively skewed surface in all cases. For the highest Reynolds numbers, the flow has values of the roughness function U + well in excess of 7 for both surfaces and the bulk flow profile has attained a constant shape across the full height of the channel except for the immediate vicinity of the roughness, which would indicate fully rough flow. However, the mean flow profile within and directly above the rough surface still shows considerable Reynolds-number dependence and the ratio of form to viscous drag continues to increase, which indicates that at least for some types of rough surfaces the flow retains aspects of the transitionally rough regime to values of U + or k + well in excess of the values conventionally assumed for the transitionally to fully rough threshold. This is also reflected in the changes that the near-wall flow undergoes as the Reynolds number increases: the viscous sublayer, within which the surface roughness is initially buried, breaks down and regions of reverse flow intensify. At the highest Reynolds numbers, a layer of near-wall flow is observed to follow the contours of the local surface. The distribution of thickness of this 'blanketing' layer has a mixed scaling, showing that viscous effects are still significant in the near-wall flow.

Rough surfaces are usually characterised by a single equivalent sandgrain roughness height scale that typically needs to be determined from laboratory experiments. Recently, this method has been complemented by a direct numerical simulation approach, whereby representative surfaces can be scanned and the roughness effects computed over a range of Reynolds number. This development raises the prospect over the coming years of having enough data for different types of rough surfaces to be able to relate surface characteristics to roughness effects, such as the roughness function that quantifies the downward displacement of the logarithmic law of the wall. In the present contribution, we use simulation data for 17 irregular surfaces at the same friction Reynolds number, for which they are in the transitionally rough regime. All surfaces are scaled to the same physical roughness height. Mean streamwise velocity profiles show a wide range of roughness function values, while the velocity defect profiles show a good collapse. Profile peaks of the turbulent kinetic energy also vary depending on the surface. We then consider which surface properties are important and how new properties can be incorporated into an empirical model, the accuracy of which can then be tested. Optimised models with several roughness parameters are systematically developed for the roughness function and profile peak turbulent kinetic energy. In determining the roughness function, besides the known parameters of solidity (or frontal area ratio) and skewness, it is shown that the streamwise correlation length and the root-mean-square roughness height are also significant. The peak turbulent kinetic energy is determined by the skewness and rootmean-square roughness height, along with the mean forward-facing surface angle and spanwise effective slope. The results suggest feasibility of relating rough-wall flow properties (throughout the range from hydrodynamically smooth to fully rough) to surface parameters.

A tiled approach to rough surface simulation is used to explore the full range of roughness Reynolds numbers, from the limiting case of hydrodynamic smoothness up to fully rough conditions. The surface is based on a scan of a standard grit-blasted comparator, subsequently low-pass filtered and made spatially periodic. High roughness Reynolds numbers are obtained by increasing the friction Reynolds number of the direct numerical simulations, whereas low roughness Reynolds numbers are obtained by scaling the surface down and tiling to maintain a constant domain size. In both cases, computational requirements on box size, resolution in wall units and resolution per minimum wavelength of the rough surface are maintained. The resulting roughness function behaviour replicates to good accuracy the experiments of Nikuradse (1933 VDI-Forschungsheft, vol. 361), suggesting that the processed grit-blasted surface can serve as a surrogate for his sand-grain roughness, the precise structure of which is undocumented. The present simulations also document a monotonic departure from hydrodynamic smooth-wall results, which is fitted with a geometric relation, the exponent of which is found to be inconsistent with both the Colebrook formula and an earlier theoretical argument based on low-Reynolds-number drag relations.

Incompressible turbulent fluid flow in aerodynamically rough channels is investigated using direct numerical simulations. A comprehensive database of simulation data for rough surfaces with different topographical properties has been developed for 17 industrially relevant rough surface samples. It includes numerous commonlyseen industrial rough surfaces such as concrete, graphite, carbon-carbon composite and ground, shotblasted and spark-eroded steel. Other surfaces such as cast, filed and gritblasted steel are also studied, along with replicas of ship propeller surfaces eroded by periods of service. The Reynolds number considered is Re τ = 180, for which the flow is in the transitionally rough regime. A study with variable δ /S q ratio while keeping S + q constant, where S q is the root mean squared roughness height, is conducted for one of the samples with the mean profiles showing convergence for δ /S q >≈ 25. A Reynolds number dependence study is conducted for two of the samples with Re τ up to 720 showing a more complete range up to the fully rough flow regime, allowing the equivalent sandgrain roughness height, k s to be computed. A correlation based on the frontal and wetted roughness area is found to be superior to the surface skewness in predicting ∆U + based on the topographic surface parameters.

Several people contributed to writing this note. Their support was invaluable.In particular, we would like to thank Esha Sarswat from the International Food Policy Research Institute (IFPRI) for her helpful comments and committed guidance.We are also grateful to Suman Chakrabarti from the University of Washington for his insightful suggestions. We would like to thank Avantika Srivastava from the Accountability Initiative and Pratima Mathews from IFPRI for editing this note. Lastly, we are indebted to Akash Singh for designing it.