Incipient motion of a non-cohesive particle under Stokes flow conditions

Erosion and deposition of sediments in the presence of shearing flows are two phenomena commonly encountered in natural, biological and industrial processes. In determining the critical conditions for the initiation of motion (onset of erosion), a force-magnitude approach has been historically used by employing either the time-averaged or the instantaneous peak fluctuating forces exerted on the sediment particles. Such approach however, has been proven to be incapable of uniquely determining the onset of sediment motion under rapidly fluctuating forces and thus alternative formulations, including impulse- and energy-based methods, have been proposed for turbulent flow conditions. Nevertheless, the force-magnitude approach, can still be applied in the case of very slow viscous flows (Stokes regime) when non-cohesive particles are considered. In the present study, we consider the problem of initiation of motion of a single mobile particle resting on a surface populated by similar types of grains and being exposed to a linear shear flow. The hydrodynamic forces and torques are computed numerically by considering Stokes flow conditions and solving the governing equations using the boundary element method (BEM). To further simplify our model, the bed substrate is parametrised by a flat wall while the pocket shielding effects are taken into account by shifting the linear shear flow towards the fluid. Subsequently, the critical conditions are uniquely determined by applying a force magnitude-based approach and considering rolling and sliding to be the possible modes of entrainment. The computed critical Shields numbers are compared to existing experimental data from the literature showing a very good overall agreement. Finally, the differences and similarities between the two extreme regimes, Stokes flow and fully rough turbulent flow threshold conditions, are briefly discussed.