Water Resources Research
Fractional transport rates are defined as the product of spatial grain entrainment, displacement length, and displacement frequency. Grain entrainment is defined relative to the population of grains on the bed surface at an initial time in order to account for partial transport, a condition in which only a portion of the exposed grains of a single size D i are mobilized over the duration of a transport event. A relation for grain displacement frequency is calculated from an assumed relation for displacement length and observed values of fractional transport rate, bed surface size distribution, and spatial entrainment in flume experiments. Fractional transport rates are independent of Di for fully mobilized fractions and decrease rapidly with D i for partially mobile fractions; the latter results from a decrease in both the displacement frequency and the mobilized proportion of each fraction. These two terms, which together determine the fractional entrainment rate, have different relations with flow strength and D i and should be independently included in a general fractional transport model. Grain-size similarity in fractional transport rates does not hold for conditions of partial transport. Partial transport is a grain-scale representation of incipient motion and can be directly related to the reference shear stress rri, a surrogate for the critical shear stress for incipient motion based on transportate rather than grain mobility. Fractional mobilization atdifferent flows may be predicted from 'rri, and partial transport appears to be the general condition at the reference transportate. Using •'ri as input, the transport component relations are used to predict the bed mobilization and fractional transportates for a field case.
Wilcock, P.R., 1997. The components of fractional transport rate, Water Resources Research, 33(1):247-258.