Tests of predicted downstream transport of clasts in turbulent flow

A theoretical prediction for the downstream transport of clasts in a turbulent flow continuum is tested by comparison with field and laboratory data. Here the downstream transport distance is deduced as a product of the distance per entrainment and the entrainment probability per unit time. The commencement of the entrainment process is treated using energetics and accounting for the interaction of eddies with bed particles, but the transport is treated conventionally using turbulent shear. The minimum energy required for entrainment is defined by the condition to lift a particle over a typical neighboring particle (or its own height). The entrainment probability is proportional to the inverse of the particle size; the transport distance is found from the settling time from the original height of entrainment, whereas the original height of entrainment is determined again by the excess energy of the collision. The distance per entrainment is found to vanish roughly as ln[(dm−d)/y0], where d is the particle diameter, dm is the diameter of the largest particle entrained, and y0 denotes the surface roughness. The effects of the logarithmic factor are to turn a relatively slowly varying function of d for small d into a very rapidly diminishing function of d as d approaches dm. The derived proportionality of dm to u∗2, the square of the friction velocity, is consistent with the Shields’ diagram for the threshold bed stress for entrainment. The theoretical result is compared with data from two field experiments and 26 lab experiments.