Abstract: Considering the random motion mechanism of splashing water droplets in the wind field around water nappes and the mechanism of Brownian random motion, we work out a physical idea－that splashing water droplets moving in the space downstream of a dam are affected by the collision of a large number of gas molecules and generate random forces. We derive a differential equation for the random motion of water droplets and obtain a mathematical expression of the diffusion coefficient using the dimensional analysis method. Then, a mathematical model for the random motion of water droplets is constructed. It is used to calculate the changes in the velocity and trajectory of water droplets under the random forces; A numerical experiment of water splashing is conducted. The splashing ranges it calculates are close to the experimental observations in previous studies, verifying its rationality and accuracy in simulating the random motion of water droplets.

Key words: splash water droplets, random force, stochastic differential equation, diffusion coefficient, splashing range, rainfall intensity