Critical Bed Shear Stress for Unisize Sediment

The overall, spatially averaged, mean magnitude of local, spatially averaged (over a small area enclosing the particlesʹ projected area), instantaneous, critical Shields shear-stress parameters required for incipient motion of uniform-sized sand grains, independent of the bed shear-velocity particle Reynolds number, equal to 0.16, is obtained from calibration of a theory for bed load sediment transport, by minimizing the sum of the squares of the deviations between theoretical and experimental bed load rates. Additionally, optimized expressions for a proposed probability density distribution of the bed shear stresses, for its standard deviation, for finite, maximum, and minimum bed shear stresses, and a bed load rate are obtained. In terms of the mean fluid shear stress, a dimensionless, critical, shear-stress parameter equal to 0.0513 is obtained. Investigation of the probability density distribution of the spatially varying, critical shear stresses would allow a more accurate formulation for the case of low transport rates.