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Reliable full-scale prediction of drag due to rough wall-bounded turbulent fluid flow remains a challenge. Currently, the uncertainty is at least 10%, with consequences, for example, on energy and transport applications exceeding billions of dollars per year. The crux of the difficulty is the large number of relevant roughness topographies and the high cost of testing each topography, but computational and experimental advances in the last decade or so have been lowering these barriers. In light of these advances, here we review the underpinnings and limits of relationships between roughness topography and drag behavior, focusing on canonical and fully turbulent incompressible flow over rigid roughness. These advances are beginning to spill over into multiphysical areas of roughness, such as heat transfer, and promise broad increases in predictive reliability.

Direct numerical simulations (DNS) are conducted for turbulent flow through pipes with three-dimensional sinusoidal roughnesses explicitly represented by body-conforming grids. The same viscous-scaled roughness geometry is first simulated at a range of different Reynolds numbers to investigate the effects of low Reynolds numbers and low R 0 /h, where R 0 is the pipe radius and h is the roughness height. Results for the present class of surfaces show that the Hama roughness function U + is only marginally affected by low Reynolds numbers (or low R 0 /h), and observations of outer-layer similarity (or lack thereof) show no signs of sensitivity to Reynolds number. Then, building on this, a systematic approach is taken to isolate the effects of roughness height h + and wavelength λ + in a turbulent wall-bounded flow in both transitionally rough and fully rough regimes. Current findings show that while the effective slope ES (which for the present sinusoidal surfaces is proportional to h + /λ + ) is an important roughness parameter, the roughness function U + must also depend on some measure of the viscous roughness height. A simplistic linear-log fit clearly illustrates the strong correlation between U + and both the roughness average height k + a (which is related to h + ) and ES for the surfaces simulated here, consistent with published literature. Various definitions of the virtual origin for rough-wall turbulent pipe flow are investigated and, for the surfaces simulated here, the hydraulic radius of the pipe appears to be the most suitable parameter, and indeed is the only virtual origin that can ever lead to collapse in the total stress. First-and second-order statistics are also analysed and collapses in the outer layer are observed for all cases, including those where the largest roughness height is a substantial proportion of the reference radius (low R 0 /h). These results provide evidence that turbulent pipe flow over the present sinusoidal surfaces adheres to Townsend's notion of outer-layer similarity, which pertains to statistics of relative motion.

[1] Global trends in a new multi-satellite surface soil moisture dataset were analyzed for the period 1988-2010. 27% of the area covered by the dataset showed significant trends (p = 0.05). Of these, 73% were negative and 27% positive. Subtle drying trends were found in the Southern US, central South America, central Eurasia, northern Africa and the Middle East, Mongolia and northeast China, northern Siberia, and Western Australia. The strongest wetting trends were found in southern Africa and the subarctic region. Intra-annual analysis revealed that most trends are not uniform among seasons. The most prominent trend patterns in remotely sensed surface soil moisture were also found in GLDAS-Noah and ERA Interim modeled surface soil moisture and GPCP precipitation, lending confidence to the obtained results. The relationship with trends in GIMMS-NDVI appeared more complex. In areas of mutual disagreement more research is needed to identify potential deficiencies in models and/or remotely sensed products.