Dynamics of Separation Points During Vertical Impact of a Floating Rectangular Cylinder
The 2D problem of the vertical separation impact of a rectangular cylinder completely immersed in an ideal, incompressible, heavy fluid is considered. It is assumed that after the impact, the cylinder moves at a constant speed into the fluid without rotation. A feature of this problem is that as a result of the impact, the liquid is separated from the solid surface with the subsequent formation of an attached cavity behind the body. The main purpose of the work is to study the process of collapse of a thin cavity at small Froude numbers corresponding to low cylinder velocities. The study of the problem is carried out using a special mathematical model based on the assumption of small perturbations of the free boundaries of the liquid. In mathematical terms, it comes down to solving a dynamic mixed boundary-value problem of potential theory with boundary conditions such as inequalities. The numerical calculations obtained on its basis are compared with the results of an asymptotic analysis of the initial nonlinear problem at small times.