Role of grain dynamics in determining the onset of sediment transport

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Sediment transport occurs when the nondimensional fluid shear stress $\Theta$ at the bed surface exceeds a minimum value $\Theta_c$. A large collection of data, known as the Shields curve, shows that $\Theta_c$ is primarily a function of the shear Reynolds number ${\rm{Re}}_*$. It is commonly assumed that $\Theta>\Theta_c({\rm{Re}}_*)$ occurs when the ${\rm Re}_*$-dependent fluid forces are too large to maintain static equilibrium for a typical surface grain. A complimentary approach, which remains relatively unexplored, is to identify $\Theta_c({\rm{Re}}_*)$ as the applied shear stress at which grains cannot stop moving. With respect to grain dynamics, ${\rm{Re}}_*$ can be viewed as the viscous time scale for a grain to equilibrate to the fluid flow divided by the typical time for the fluid force to accelerate a grain over the characteristic bed roughness. We performed simulations of granular beds sheared by a model fluid, varying only these two time scales. We find that the critical Shields number $\Theta_c({\rm Re}_*)$ obtained from the model mimics the Shields curve and is insensitive to the grain properties, the model fluid flow, and the form of the drag law. Quantitative discrepancies between the model results and the Shields curve are consistent with previous calculations of lift forces at varying ${\rm Re}_*$. Grains at low ${\rm Re}_*$ find more stable configurations than those at high ${\rm{Re}}_*$ due to differences in the grain reorganization dynamics. Thus, instead of focusing on mechanical equilibrium of a typical grain at the bed surface, $\Theta_c({\rm{Re}}_*)$ may be better described by the stress at which mobile grains cannot find a stable configuration and stop moving.