Purely erosional cyclic and solitary steps created by flow over a cohesive bed

Gary Parker, Norihiro Izumi

Research output: Contribution to journalArticlepeer-review


An erodible surface exposed to supercritical flow often devolves into a series of steps that migrate slowly upstream. Each step delineates a headcut with an associated hydraulic jump. These steps can form in a bed of cohesive material which, once eroded, is carried downstream as washload without redeposition. Here the case of purely erosional, one-dimensional periodic, or cyclic steps in cohesive material is considered. The St. Venant shallow-water equations combined with a formulation for sediment erosion are used to construct a complete theory of the erosional case. The solution allows wavelength, wave height, migration speed and bed and water surface profiles to be determined as functions of imposed parameters. The analysis also admits a solution for a solitary step, or single headcut of self-preserving form.

Original languageEnglish (US)
Pages (from-to)203-238
Number of pages36
JournalJournal of Fluid Mechanics
StatePublished - Jan 1 2000
Externally publishedYes

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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