Sand transport model of barchan dune equilibrium



Erosion and deposition over a barchan dune near the Salton Sea, California, is modelled by book-keeping the quantity of sand in saltation following streamlines of transport. Field observations of near-surface wind velocity and direction plus supplemental measurements of the velocity distribution over a scale model of the dune are combined as input to Bagnold-type sand-transport formulae corrected for slope effects. A unidirectional wind is assumed. The resulting patterns of erosion and deposition compare closely with those observed in the field and those predicted by the assumption of equilibrium (downwind translation of the dune without change in size or geometry). Discrepancies between the simulated results and the observed or predicted erosional patterns appear to be largely due to natural fluctuation in the wind direction. Although the model includes a provision for a lag in response of the transport rate to downwind changes in applied shear stress, the best results are obtained when no delay is assumed.

The shape of barchan dunes is a function of grain size, velocity, degree of saturation of the oncoming flow, and the variability in the direction of the oncoming wind. Smaller grain size or higher wind speed produce a steeper and more blunt stoss-side. Low saturation of the inter-dune sandflow produces open crescent-moon-shaped dunes, whereas high saturation produces a whaleback form with a small slip face. Dunes subject to winds of variable direction are blunter than those under unidirectional winds.

The size of barchans could be proportional to natural atmospheric scales, to the age of the dune, or to the upwind roughness. The upwind roughness can be controlled by fixed elements or by the sand is saltation. In the latter case, dune scale may be proportional to wind velocity and inversely proportional to grain size. However, because the effective velocity for transport increases with grain size, dune scale may increase with grain size as observed by Wilson (1972).