Preprints
https://doi.org/10.5194/esurf-2020-44
https://doi.org/10.5194/esurf-2020-44

  22 Jun 2020

22 Jun 2020

Review status: a revised version of this preprint was accepted for the journal ESurf and is expected to appear here in due course.

Controls on the hydraulic geometry of alluvial channels: bank stability to gravitational failure, the critical-flow hypothesis, and conservation of mass and energy

Jon D. Pelletier Jon D. Pelletier
  • Department of Geosciences, The University of Arizona, 1040 East Fourth Street, Tucson, Arizona 85721–0077, USA

Abstract. The bankfull depths, widths, depth-averaged water velocities, and along-channel slopes of alluvial channels are approximately power-law functions of bankfull discharge across many orders of magnitude. What mechanisms give rise to these patterns is one of the central questions of fluvial geomorphology. Here it is proposed that the bankfull depths of alluvial channels are partially controlled by the maximum heights of gravitationally stable channel banks, which depend on bank material cohesion and hence on clay content. The bankfull depths predicted by a bank-stability model correlate with observed bankfull depths estimated from the bends in the stage-discharge rating curves of 387 U.S. Geological Survey gaging stations in the Mississippi River Basin. It is further proposed that depth-averaged water velocities scale with bankfull depths as a result of a self-regulatory feedback among water flow, relative roughness, and channel-bed morphology that limits depth-averaged water velocities to be within a relatively narrow range associated with Froude numbers that have a weak inverse relationship to bankfull discharge. Given these constraints on channel depths and water velocities, bankfull widths and along-channel slopes consistent with observations follow by conservation of mass and energy of water flow.

Jon D. Pelletier

Jon D. Pelletier

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Short summary
The sizes and shapes of alluvial channels vary in a systematic way with the water flow they must convey during large floods. It is demonstrated that the depth of alluvial channels is controlled by the resistance of channel bank material to slumping which in turn is controlled by clay content. Deeper channels have faster water flow in a manner controlled by a critical hydraulic state to which channels tend to evolve. Channel width and slope can be further quantified using conservation principles.