‘Bedload’ dynamics: Grain impacts,momentum transfer and derivation of a grain froude number

A test is proposed for Bagnold's postulate that the normal weight stress due to moving ‘bedload’ is balanced by a solid transmitted stress due to the rate of change of momentum produced by grain impacts on unit area of the stationary bed. The test involves derivation of an expression for normal momentum transfer due to saltating grains at moderate transport stages when grain-to-grain collisions and partial suspension during saltation may be ignored. A dimensionless number, Φ, (a grain Froude Number) is derived, given by ū²/g where ū is the mean grain forward velocity, g is the gravitational acceleration and L? is the length of a single saltation ‘jump’. Equilibrium demands that Φ be unity during bedload transport involving saltating grains if Bagnold's postulate is correct. Experimental data shows Φ < 1, the discrepancy between theory and experiment being due to the existence of lift forces acting upon bedload grains. Bagnold's postulate is correct for concentrated dispersions of grains, as in grain flows, when fluid lift forces may be neglected due to high particle concentration.