Abstract: Aiming at the scientific problem of the random motion mechanism of splashing water droplets in the wind field of water mouth, based on the mechanism of Brownian random motion, the physical idea that splashing water droplets moving in the downstream space of the dam will be affected by the collision of a large number of gas molecules and generate random forces is proposed. The random differential equation of water droplets moving in the downstream space is established, and the mathematical expression of the diffusion coefficient is obtained by dimensional analysis method. Then the mathematical model of random motion of water droplets is established. The model was used to calculate the changes of the velocity and trajectory of water droplets under the action of random forces, and the splashing experiment was numerically simulated. The calculated splashing range was closer to the experimental observation value, which verified the rationality and correctness of the mathematical model of the random motion of water droplets.