Схлопывание присоединенной каверны при малых числах Фруда после отрывного удара плавающего эллиптического цилиндра

Abstract

The plane problem of the collapse of an attached cavity formed as a result of a separation impact of an elliptical cylinder under the free surface of a heavy fluid is considered. It is assumed that after the impact the cylinder moves horizontally with constant velocity. At small Froude numbers, which correspond to small velocities of the cylinder, the free boundaries of the liquid are slightly perturbed and the process of cavity collapse is mainly reduced to the study of dynamics of breakaway points. The solution to this problem is constructed using asymptotic decompositions on a small parameter, which is the Froude number. In the main asymptotic approximation, the mixed boundary value problem of potential theory with one-sided restrictions on the body surface is formulated. On its basis, the dynamics of detachment points, the shape of a thin cavities, and the reaction of the environment to the body are determined. The results obtained can be used for solving practical problems of marine and ship hydrodynamics.