Fall velocities of saltating sand grains in air and their distribution laws

In a cloud of blowing sand, collisions between falling sand grains and the sand bed are an important process that is the main source of additional saltating sand grains, because the collision process transfers momentum to the sand bed and initiates the liftoff of new sand grains. The initial liftoff and fall velocities of saltating sand grains are key parameters in the collision process, but little information exists on the subsequent fall velocities of the saltating sand grains. One important reason for this lack is that the collision process is unclear. Based on experimental data from high-speed multi-flash photographic images obtained in a wind tunnel and on a motion model of saltating sand grains, this paper discusses the fall velocities of saltating sand grains and the corresponding velocity frequency distributions. The results demonstrate that fall angles are small (less than 20°), and decrease with increasing frictional wind velocity. The vertical component of fall velocity increases with increasing frictional wind velocity, and is consistent with the initial vertical liftoff velocity. The fall angle and vertical velocity both follow a gamma distribution. The horizontal fall velocity mainly determines the resultant fall velocity, and both increase with increasing frictional wind velocity. The horizontal and resultant fall velocities follow a Pearson IV distribution. These results improve our understanding of the collision process between falling sand grains and sand beds and will also help us to modify the splash function that connects the parameters of falling saltating sand grains and their initial liftoff parameters.