Threshold of aeolian and fluvial nonsuspended sediment transport along arbitrarily sloped beds from an analytical model of periodic grain motion

The downslope component of the gravitational force affects the threshold and direction of sediment transport along an arbitrarily sloped bed. It plays an important role for the shape and stability of river channels, and for the formation, evolution, and morphology of aeolian and fluvial bedforms. Here, we generalize an existing model of the threshold of nonsuspended sediment transport, which unifies aeolian and fluvial transport conditions using an analytical description of flow-driven periodic grain motion, to account for arbitrarily sloped beds. Without any readjustment of the model parameters, the generalized model captures the experimentally measured bed slope effect on the transport threshold much better than previously proposed models based on incipient grain motion, especially for large bed slopes in the direction transverse to the driving flow. This is mostly because drag resistance counteracts the transverse average motion of transported grains, which in the model has the same mathematical effect as a reduction of the transverse bed slope. For aeolian transport, the model predicts substantial gravity-induced transverse diffusion of saltating grains, neglected in previous studies, which may explain why aeolian barchan dunes generally tend to have a larger width than length.