Hydraulic resistance in open-channel flows over self-affine rough beds

Knowledge of hydraulic resistance of single-valued self-affine fractal surfaces remains very limited. To advance this area, a set of experiments have been conducted in two separate open-channel flumes to investigate the effects of the spectral structure of bed roughness on the drag at the bed. Three self-affine fractal roughness patterns, based on a simple but realistic three-range spectral model, have been investigated with spectral scaling exponents of −1, −5/3 and −3, respectively. The different widths of the flumes and a range of flow depths also afforded an opportunity to consider effects of the flow aspect ratio and relative submergence. The results show that with all else equal the friction factor increases as the spectral exponent decreases. In addition, the relationship between the spectral exponent and effective slope of the roughness is demonstrated, for the first time. Aspect ratio effects on the friction factor within the studied range were found to be negligible.