A physical model of wind-blown sand transport

Eolian saltation, the transport of sand by the wind, involves a variety of physical processes. A fundamental understanding of saltation requires an analysis starting from the level of the individual sand grain. The complexity of this nonlinear dynamical system compels us to divide the problem into more easily handled decoupled components: the saltating grain-bed impact process, the force of the wind on individual grains, the determination of the wind profile from the spatially averaged force of the moving grains on the air, and the formation of small-scale bedforms: ripples. The impact of a moving sand grain with a bed of sand is studied with two-dimensional dynamical computer simulations and an experiment propelling single grains onto a sand bed. We find that the result of the impact may be described in terms of the rebound of the incident particle and the ejection of bed grains. The bed grain ejections originate from a localized area around the impact point, and at steps in the surface (elevation changes of one grain diameter) which are more widely distributed; these surface steps we term brinks (downstream-facing) and anti-brinks (upstream-facing). A model for steady-state saltation is proposed which incorporates both aerodynamics and the mechanics of the grain-bed impacts, and balances the losses of saltating particles on impact with the bed by gains due to impact generated bed grain ejections. This model does not require data on blowing sand. Results are obtained which qualitatively agree with existing data. Quantitative tests will require new experiments. We argue that grain-bed impacts, not fluid stresses, are the means for entraining grains in steady-state eolian saltation. The development of sand surface topography is viewed as a result of surface grain transport (reptation) driven by the impact of high-energy saltating grains onto the bed. The collision and merger of small collections of sand, proto-ripples, lead to the asymptotic development of uniform ripples from an initially smoothed surface. The limiting wavelength is pictured as being determined by statistical fluctuations in the saltating impact flux and/or the shortening of the saltation shadow zone below the mean reptation length during a collision between two ripples. Field observations of developing ripple cross-sectional shapes confirm these ideas qualitatively, and rough calculations of limiting wavelengths agree with existing data.