Estimating the windward slope profile of a barchan dune

A new theoretical scheme is presented to model the shape of a sand dune at equilibrium that does not require iterative calculations of the interaction between the wind flow and topography. The model is constructed by incorporating theory based on aerodynamics into a grain-scale model that estimates the shear velocity at the dune crest through the calculation of the sand trapping efficiency of the slipface in the lee of the dune. Published field data, collected in southern Peru, California and southern Morocco, show that as a dune becomes higher the windward slope becomes steeper. For the model proposed, the wind flow over a dune was first assumed to be similar to that over a Gaussian hill. By further assuming a fixed shear velocity on the level surface, the windward slope angle and migration speed of dunes in southern Peru can be explained. To comply with all available data, some aspects are still open to further investigation. However the theoretical insight presented herein implies that the upper limit of dune height may be greater in windier environments.