Mathematical Model of a Post-Impact Cavitational Deceleration of a Torus in a Liquid

Аннотация

The process of cavity formation under a vertical impact and subsequent braking of a torus of an elliptical cross section semisubmerged in a liquid is investigated. The solution of the problem is constructed by the direct asymptotic method, which is effective at short time periods. A special problem with unilateral constraints is formulated based on which the initial zones of separation and contact of liquid particles, as well as perturbations of the internal and external free boundaries of the liquid at short time periods, are determined. Limit cases of a degenerate and a thin torus are considered. In the case of a thin torus, the flow pattern corresponds to the 2D problem of the cavitational braking of an elliptical cylinder in a liquid after a continuous impact.