Entrainment threshold of cohesionless sediment grains under steady flow of air and water

Existing formulations for bed sediment entrainment under steady flow are incapable of explaining two well-documented observational facts: (i) water flow requires considerably higher dimensionless shear stresses to move the bed grains than air flow; and (ii) under open channel flow, steep granular beds are more stable than beds with milder slopes. These two facts, together with recent direct measurements of forces acting on bed grains giving time-mean negative drags (Schmeeckle et al., 2007), question the conventional models of forces used so far. Here, fluid forces acting on bed particles are treated in a new way in order to take into consideration the fundamental interference effects, thus obtaining appropriate magnitude estimates that exhibit good agreement with direct force measurements by Schmeeckle et al. (2007). Impulsive pressure fluctuations generated by turbulence are shown to be capable of dislodging the bed grains by saltation under air flow, whereas they can only produce a rocking effect under water flow, thus explaining the first anomaly. On the other hand, previous work by the authors allows a direct estimate of space averaged time-mean drag and lift forces exerted on bed grains. Both components have the same order of magnitude but, contrary to the common belief, the mean lift is downward, which provides an explanation for the second anomaly. Finally, spatial disturbances of pressure, both positive and negative, appear to generate maximum, persistent, local forces considerably greater than mean forces, thus allowing an explanation for the observed negative time-mean drag. A new formula for predicting incipient motion of sediment under open channel flow is derived, which incorporates all dynamically significant effects and gives very good agreement with observation for the entire range of bed slopes.