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?θc/θ, θ = dimensionless bed-shear stress; and θc = critical value of θ at which grains begin to move. The equation shows that θt, which is the value of θ at the onset of the sheet-flow regime and is assumed to occur when Pb = 1, is around 0.5 with the exact value controlled by θc. For example, when θc = 0.045, θt = 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.