Probability distribution functions for the initial liftoff velocities of saltating sand grains in air

Saltating sand grains are the primary component of airborne sand and account for 75% of all transport flux of sand grains. Although they have been widely studied, the microscopic and macroscopic aspects of blown sand physics have not been united, and this has slowed development of this field. The main reason for this is that the bridge ( probability distribution functions for initial liftoff velocities of saltating sand grains) between the macroscopic and microscopic research has not been satisfactorily solved because it is difficult to measure the initial liftoff parameters of saltating sand grains and because the underlying theory is lacking. In this paper, we combined theoretical analyses with wind tunnel experiment data to describe the liftoff parameters of saltating sand grains (the horizontal, vertical, and resultant liftoff velocities and angles). On the basis of these data, the liftoff angles follow a LogNorm4 distribution function, whereas the horizontal, vertical, and resultant liftoff velocities follow a Gamma distribution function. We also demonstrated that it is feasible to colligate initial liftoff velocities of saltating sand grains obtained under different frictional wind velocities by different scholars in wind tunnel experiments and comprehensively analyze their distributions. Therefore the distribution functions of initial liftoff velocities of saltating sand grains presented in this paper do a good job of reflecting the underlying physics.