A model of the trajectories and midair collision probabilities of sand particles in a steady state saltation cloud

Abstract

To estimate the probability of a midair interparticle collision for a 0.25 mm saltating particle in a steady state saltation cloud, a physical model that can predict this probability is developed. In our model a set of experimentally determined saltation cloud wind profiles, which are notably nonlogarithmic, are employed. First, the trajectories of a saltating particle with different lift‐off velocities and at different free‐stream wind velocities are calculated using the wind profile results, and they are compared to corresponding trajectories calculated by logarithmically distributed wind profiles. Our model yields trajectory heights and lengths that are much different than those calculated by the logarithmically distributed profiles. Second, the midair interparticle collision probability is simulated for its ascending and descending stages, as well as for its entire trajectory. Finally, by considering the probability density function the collision probabilities of a saltating particle with a random lift‐off velocity at several friction velocities of wind are calculated. The results show that the probability of such a collision almost linearly increases with the friction velocity of wind, and it can reach as high as 0.34 when the friction velocity of wind is 1.2 m/s. Therefore the effect of midair collision should not be neglected in the saltation model, especially at high‐friction velocities of wind.