Criteria for incipient motion of spherical sediment particles

Initiation of bed-load transport of uniform spherical sediment particles on a horizontal bed in an open-channel flow is studied. On the basis of micromechanical and fluid dynamical considerations, two separate criteria for the initiation of motion are derived: one for rolling and one for lifting. Fluid forces such as drag, shear lift, Magnus lift, and lift due to centrifugal force are included in the derivation. The formulation of the lift force is theoretical. No empirical coefficient is used other than the drag coefficient C _d, which is well established in the literature. In the low particle Reynolds number regime, where u_*d/ν ≤ 1, the dimensionless stress required to initiate lifting is found to be much higher than that of rolling, the former substantially above the Shields' curve while the latter is substantially below it. The theory is compared with Vanoni's 1964 data, with meaningful results. For higher particle Reynolds number, where u_*d/ν> 10, the dimensionless stress needed to initiate lifting is closer to that of rolling. The Shields' curve for the most part lies between the two theoretical thresholds.