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 P-b representing the proportion of grains on the bed that are entrained as bed load. The model yields the equation P-b=2.56 theta G(3) in which G =1 - theta(c)/theta, theta = dimensionless bed-shear stress; and theta(c)= critical value of Oat which grains begin to move. The equation shows that theta(t), which is the value of theta 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 theta(c). For example, when theta(c) = 0.045, theta(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 theta 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.