A bed-load transport model for rough turbulent open-channel flows on plane beds

Athol D. Abrahams, Peng Gao

Research output: Contribution to journalArticlepeer-review

42 Scopus citations


Data from flume studies are used to develop a model for predicting bed-load transport rates in rough turbulent two-dimensional open-channel flows moving well sorted non-cohesive sediments over plane mobile beds. The object is not to predict transport rates in natural channel flows but rather to provide a standard against which measured bed-load transport rates influenced by factors such as bed forms, bed armouring, or limited sediment availability may be compared in order to assess the impact of these factors on bed-load transport rates. The model is based on a revised version of Bagnold's basic energy equation Ibsb = ebω, where ib is the immersed bed-load transport rate, w is flow power per unit area, eb is the efficiency coefficient, and sb is the stress coefficient defined as the ratio of the tangential bed shear stress caused by grain collisions and fluid drag to the immersed weight of the bed load. Expressions are developed for sb and eb in terms of G, a normalized measure of sediment transport stage, and these expressions are substituted into the revised energy equation to obtain the bed-load transport equation ib = ω G3.4. This equation applies regardless of the mode of bed-load transport (i.e. saltation or sheet flow) and reduces to ib = ω where G approaches 1 in the sheet-flow regime. That ib = w does not mean that all the available power is dissipated in transporting the bed load. Rather, it reflects the fact that ib is a transport rate that must be multiplied by sb to become a work rate before it can be compared with w. It follows that the proportion of ω that is dissipated in the transport of bed load is ibsb/ω, which is approximately 0.6 when ib = ω. It is suggested that this remarkably high transport efficiency is achieved in sheet flow (1) because the ratio of grain-to-grain to grain-to-bed collisions increases with bed shear stress, and (2) because on average much more momentum is lost in a grain-to-bed collision than in a grain-to-grain one.

Original languageEnglish (US)
Pages (from-to)910-928
Number of pages19
JournalEarth Surface Processes and Landforms
Issue number7
StatePublished - Jun 2006


  • Bed-load transport
  • Saltation
  • Sediment transport
  • Sheet flow

ASJC Scopus subject areas

  • Geography, Planning and Development
  • Earth-Surface Processes
  • Earth and Planetary Sciences (miscellaneous)


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