Transition between two bed-load transport regimes: Saltation and sheet flow

In the saltation regime where bed-shear stress is low, bed load moves by sliding, rolling, and saltating along the bed, while in the sheet-flow regime where bed-shear stress is high, it travels by a combination of saltation and sheet flow. In this paper a theoretical model is developed for predicting the onset of the sheet-flow regime as shear stress increases. This model is based on a new variable Pb representing the proportion of grains on the bed that are entrained as bed load. The model yields the equation Pb=2.56θG³ in which G=1-θ_c/θ, θ=dimensionless bed-shear stress; and θ_c=critical value of θ at which grains begin to move. The equation shows that θ_t, which is the value of θ at the onset of the sheet-flow regime and is assumed to occur when P_b=1, is around 0.5 with the exact value controlled by θ_c. For example, when θ_c=0.045, θ_t=0.52. The theoretical model is verified by performing a nonlinear regression analysis on data from 285 flume experiments. Additional flume experiments with a high-speed video (HSV) system result in consistent values of θ for the onset of the sheet-flow regime, which support the theoretical model. The HSV images further reveal that: (1) the sheet-flow regime is characterized by granular sheets or laminations; and (2) a zone of mixed saltation and rolling grains exists not only in the saltation regime but also in the sheet-flow regime.