Asymptotics of slow motions of a rectangular cylinder in a liquid after a separation impact

The process of collapse of a cavern, which is formed following the separation impact produced by a rectangular cylinder in an ideal, incompressible, and heavy liquid, was studied. Assuming that the speed of the cylinder is low, asymptotics of the main characteristics of the impact were constructed. The difficulties arising in this case are mainly related to the fact that the dynamics of the separation points is not known in advance and depends on a small parameter, i.e., on the dimensionless velocity of the cylinder. With the help of a special change of variables, the matter was reduced to the study of a problem with the dynamics of separation points corresponding to the leading approximation independent of the indicated parameter. This enabled us to determine the second term of the asymptotics with account for the nonlinear terms in the model. In the leading approximation, a problem with a free boundary, which is similar to the classical model of an impact with separation at each fixed moment of time, was formulated. On the basis of the first two terms of the asymptotics, the process of collapse of the cavern was described with allowance for the rise of the inner free boundary of the liquid. Comparison with the previously obtained results was carried out.