Vertical profiles of mass flux for windblown sand movement at steady state

A profile pattern different from the generally accepted one that mass flux exponentially decreases with the height is indicated by several experimental and theoretical studies and field observations on aeolian sediment transports; however, a theoretical explanation for such a pattern is still absent. To overcome this difficulty, a new model is suggested in this paper, in which the interaction between the saltation of sand grains and the winds is considered, the probability distribution function of vertical liftoff velocities of grains is used to obtain all probable trajectories of saltating grains, and the steady state of the windblown sand movement is reached by adjusting the surface ejection flux (the number ejected per unit area of the bed per unit time). The validity of the model is confirmed by comparing the numerical results of streamwise sand transport versus wind velocity with those calculated from the well-known empirical formulas of Bagnold and Kawamura in their respective effective regions and by comparing the mass flux profile with Yin's observation in the gravel desert. The vertical profile of the mass flux of windblown sand movement obtained obviously displays a stratification pattern composed of a linear increment layer, a saturation layer, and a monotonic decrement layer. The numerical results also elucidate that the stratification patterns of the steady mass flux profiles are not influenced by the electrification force, the wind velocity, and the distributions of vertical liftoff velocities of sand grains, while the peak value of mass flux may occur at different heights, and tend to shift upward with increasing wind velocity.