Transport Formula for Collisional Sheet Flows with Turbulent Suspension

The prediction of the transport of sediments in streams is of crucial importance for many geophysical and industrial applications. Most of the available formulas for sediment transport are empirical and apply to situations near initiation, where a few erratic particles are seen jumping and rolling over an immobile bed. However, they are commonly adopted for predicting massive transport of sediments, although more rigorous approaches exist. The latter make use of constitutive relations from kinetic theories of granular gases, but require the numerical integrations of complicated, nonlinear differential equations, hence discouraging their usage for practical purposes. A new, explicit formula for predicting intense sediment transport is proposed here, based on kinetic theories of granular gases and incorporating in a simple yet rigorous way the possibility of turbulent suspension of the particles. It is shown that this formula, unlike others, can quantitatively reproduce physical experiments on steady, uniform flows of natural and artificial particles and water over horizontal, movable beds taken from the literature. These findings suggest that granular physics is now mature enough to provide practical tools in fields that were so far mainly empirically oriented.