The Role of Grain Dynamics in the Onset of Sediment Transport

Despite decades of research, the grain-scale mechanisms that control the onset of sediment transport are still not well understood. A large collection of data, known as the Shields curve, shows that Θ _c, which is the minimum dimensionless shear stress at the bed for grains to move, is primarily a function of the shear Reynolds number Re_*. To understand this collapse, it is typically assumed that the onset of grain motion is determined by the conditions at which fluid forces violate static equilibrium for surface grains. Re_* compares the grain size to the size of the viscous sublayer in the fluid flow, so the relevant fluid lift and drag forces vary with Re_*. A complimentary approach, which remains relatively unexplored, is to ask instead when mobilized grains can stop. In this case, Re_* is the ratio of two important time scales related to grain motion: (1) the time for a grain to equilibrate to the fluid flow and (2) the time for the shear stress to accelerate a grain over the characteristic bed roughness. Thus, Re_* controls whether grains are accelerated significantly between collisions with the bed. To test how this effect relates to the Shields curve, we perform simulations of granular beds sheared by a model fluid flow, where Re_* is varied only through the fluid-grain coupling, which alters the grain dynamics. We find good qualitative agreement with the Shields curve, and the quantitative discrepancies are consistent with lift forces calculations at varying Re_*. Our results suggest that the onset of sediment transport may be better described as when mobile grains are able to stop, which varies significantly with Re_*, and theoretical descriptions that account for this effect may be more successful than those that consider only static equilibrium.