On the crescentic shape of barchan dunes

Aeolian sand dunes originate from wind flow and sand bed interactions. According to wind properties and sand availability, they can adopt different shapes, ranging from huge motion-less star dunes to small and mobile barchan dunes. The latter are crescentic and emerge under a unidirectional wind, with a low sand supply. Here, a 3d model for barchan based on existing 2d model is proposed. After describing the intrinsic issues of 3d modeling, we show that the deflection of particules in reptation due to the shape of the dune leads to a lateral sand flux deflection, which takes the mathematical form of a non-linear diffusive process. This simple and physically meaningful coupling method is used to understand the shape of barchan dunes.