Periodic saltation over hydrodynamically rough beds: aeolian to aquatic

We determine approximate analytical solutions for average periodic trajectories of particles that are accelerated by the turbulent shearing of a fluid between collisions with a hydrodynamically rough bed. We indicate how the viscosity of the fluid may influence the collisions with the bed. The approximate solutions compare well with periodic solutions for average periodic trajectories over rigid bumpy and erodible beds that are generated numerically. The analytic solutions permit the determination of the relations between the particle flux and the strength of the shearing flow over a range of particle and fluid properties that vary between those for sand in air and sand in water.