A Similarity Theory for Saltation and Application to Aeolian Mass Flux

Abstract

A similarity theory for saltation is presented. To derive the theory, a saltation model is developed and applied to simulating particle motion in turbulent flows. The numerical results are then fitted to simple ‘universal’ expressions, or similarity functions. This approach allows the determination of saltation mass flux and other quantities. While the theory can be general, we focus on studying the saltation mass flux profile q(z). It is shown that q(z) is determined by friction velocity, aerodynamic roughness length and soil particle size distribution. There are two limiting situations, i.e., the saltation of large particles in weak turbulence and that of small particles in strong turbulence, for these two cases, q(z) is respectively exponential and Gaussian. Modified saltation has an intermediate saltation mass flux profile. For multi-sized particles, q(z) is a weighted superposition of many different profiles. The theory is compared with wind-tunnel observations, and uncertainties of the theory are discussed.