“…The water-entry problem exists in many engineering fields, such as water entry of vehicles, the airdrop of aircraft, the water landing of seaplanes and spacecraft and the wave slamming of ships, etc. (Seddon & Moatamedi 2006;Fang et al 2022;Ju et al 2023;Kong et al 2023;Sun et al 2023;Zhao, Yang & Ming 2023a). High-speed water entry is a transient and strongly nonlinear process involving crossing air and water interfaces, and many complex flows, such as violent water surface splashing and various characteristics of cavity evolution, always occur; these flows are strongly related to the strong impact loads and drastic motions of the body entering the water (Truscott, Epps & Belden 2014;Shi, Hua & Pan 2020;Sui et al 2023).…”