Abstract: The velocity distribution of saltating sand grains is the bridge between macroscopic and microscopic aeolian research, which largely affects the saltating trajectory and mass flux profile. However, the relation between probability distribution of impacting speed and that of impacting angle remains unclear. In this paper, velocity of saltating sand grains in wind-blown sand located at 0.001 m above the sand bed was measured using a phase Doppler particle analyzer in a wind tunnel. The joint probability distribution of impacting speed and angle is studied by analyzing the probability distribution of impacting angle under each impacting speed. The results show that the probability distribution of impacting speed can be expressed as a lognormal function, while that of impacting angle follows an exponential function. The probability distribution of impacting angle conditioned for each impacting speed also follows an exponential function, whose slope becomes steeper with increasing impacting speed. This implies that the probability distributions of impacting speed and impacting angle are strongly dependent on each other. In the end, we present functions to describe the independent and conditional joint probability distributions of the impacting speed and angle of saltating sand grains.

Key words: saltating movement, sand speed, joint probability distribution, sand mass flux