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

Mark T. Stewart* (Corresponding Author), Stuart M. Cameron, Vladimir I. Nikora, Andrea Zampiron, Ivan Marusic

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)
18 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)183-169
Number of pages14
JournalJournal of Hydraulic Research
Issue number2
Early online date4 Jul 2018
Publication statusPublished - 2019

Bibliographical note

The authors wish to express their gratitude to Stephan Spiller for advice regarding the silicone moulds, to Cameron Scott for assisting with manufacturing of the roughness elements and Davide Collautti for help with conducting experiments.


  • Bed roughness
  • Drag coefficient
  • Hydraulic resistance
  • Open channel flow turbulence
  • self affine fractal surface
  • hydraulic resistance
  • drag coefficient
  • open-channel flow turbulence
  • self-affine fractal surface


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