Predicting incipient motion, including the effect of turbulent pressure fluctuations in the bed

Incipient motion of particles on a river bed can, in principle, be understood and predicted from a balance of the forces acting on the particles. On a natural river bed the exposure of particles to the flow is variable. The effect of exposure on the initiation of motion, including the case of deep embedding, is studied in this paper. So far, the turbulence-induced lifting force has been derived exclusively from examinations of the surface flow. The understanding of destabilization processes of the riverbed is improved when turbulence-induced vertical pressure gradients in the upper sediment layer are included. This is particularly important for particles that lie in the lee of larger ones. An analytical solution for the critical Shields parameter of spherical particles is found, including the effects of pressure fluctuations in the bed, macroscale flow structures, average bed slope, and shallow flow. Existing laboratory data designed to test the effect of exposure and roughness conditions are in excellent agreement with the new model.