Effects of the Magnus and Saffman forces on the saltation trajectories of sand grain

Saltating sand grains are the primary component of airborne sand and account for 75% of all sand transport flux. The saltation height and horizontal distance traveled by sand grains are key factors in sand-control engineering. In addition to gravity and aerodynamic drag, the Magnus and Saffman forces also play important roles in saltation. To quantify the magnitudes of these forces in saltation we used high-speed multi-flash photography to observe the movement of saltating sand grains in a wind tunnel; this proved to be an efficient technique for determining the movement and rotational velocities of grains of natural sand with grain sizes ranging from 0.2 to 0.3 mm and shear velocities (u⁎) of 0.67, 0.83, and 0.87 m s− 1. The rotational speed of saltating sand grains varied between 200 and 800 rev s− 1; mean clockwise and anticlockwise rotational speeds were nearly identical, and both increased with increasing saltation height. With saltation heights divided into 1 cm intervals, the rotational speeds followed a Lorentzian distribution. Calculations based on a saltation model showed that the maximum increases in saltation height and in horizontal distance due to the Magnus force were 10.2 and 24.9%, respectively. The rate of increase of both parameters increased with increasing lift-off angle. The maximum increases in saltation height and horizontal distance of sand grains caused by the Saffman force were only 4.6% and 3.7%, respectively.