Criteria for the instability of upper-stage plane beds

Calculations of the critical dimensionless bed stresses that obtain when upper-stage plane beds should revert to ripple and dune bed forms are presented. Strong support is given to the Bagnold ‘universal’ plane-bed instability criterion and to a modified criterion suggested by Allen over a wide range of solids grain size. A reinterpretation of the mechanism of plane bed instability is based upon the extent to which significant grain concentrations in plane bed flows increase apparent fluid viscosity and decrease turbulence production over potential bed defects, thereby preventing ripple or dune propagation and growth.