Asymptotic theory of liquid-solid impact

The liquid–solid impact problem is analysed with the help of the method of matched asymptotic expansions. This method allows us to estimate the roles of different effects (viscosity of the liquid, surface tension, compressibility, nonlinearity, geometry) on the impact, to distinguish the regions of the flow and the stages of the impact, where and when each of these effects is of major significance, to present a complete picture of the flow, and describe approximately such phenomena as jetting, escape of the shock onto the liquid–free surface and cavitation. Five stages of the impact are distinguished: supersonic stage, transonic stage, subsonic stage, inertia stage and the stage of developed liquid flow. The asymptotic analysis of each stage is based on general principles of hydrodynamics and will be helpful to design experiments on liquid impact and to develop an adequate computational algorithm, as well as to understand the dynamics of the process.