Abstract: A large number of water droplets are splashed out after a water jet nappe impinging into the free surface of a water body downstream of the dam. To address the low computational efficiency in solving the random water droplet splashing mathematical model, this paper describes an approximate analytical method for calculating the landing locations of the splashed droplets, based on two-dimensional projectile motions against secondary resistance. We compare the calculations of landing locations and probability density distributions with those of the fourth-order Runge-Kutta method. Notably, given the same number of water droplets and initial information, our new method achieves an accuracy comparable to the Runge-Kutta and a significant reduction in computational cost—only 1/30 of the latter one, thus offering an efficient approach for analysis of the motions of randomly sprayed water droplets.

Key words: flood discharge atomization, splashing water droplets, random splashing model of water droplets, landing location, approximate analytical method