Movability Number as the Parameter of Sediment Incipient Motion: A Mathematical Approach

In fluvial sediment transport, the sediment threshold parameter Movability Number, which is the ratio of the shear velocity and the settling velocity of a sediment particle, is seen as a potential replacement for the traditional Shields parameter. Until now, the studies carried out on Movability Number have been mostly empirical or crudely analytical. In the current study, a mathematical modeling approach is attempted. Steady unidirectional flow is considered and the mode of entrainment is taken as that of rolling, with a compact sediment bed. The mathematical relationships developed here express the Movability Number as a function of either shear Reynolds number or dimensionless grain diameter. Comparisons are made with both experimental data and previous empirical formulae. The developed model is a novel approach to study the Movability Number, which bears satisfactory nearness to the previous studies. The deviation produced in terms of underestimation is due to the rolling mode of motion, which requires the least disturbing energy. The developed model can be improved by the consideration of turbulence in future studies.