Strong expansion–contraction of a cavity in a fluid under acoustic action

The simplest model of the strong expansion–contraction of a spherical evacuated cavity in an unbounded ideal incompressible fluid under acoustic action is constructed. It is assumed that the cavity is formed at the instant of maximum dilatation of the fluid as the result of the breakdown in its continuity by elementary particles, and the amplitude of the induced acoustic oscillations exceed the mean pressure in the fluid by an order of magnitude or more. The trajectory of the motion of the interface is divided into three stages, in each of which it is assumed that there is a certain constant value of the pressure. This enables an approximate analytical solution of the problem to be obtained. It is shown that there is an agreement with the numerical solution of the initial problem that is sufficient for qualitative estimates. The solution obtained enables a parametric analysis of the expansion–contraction processes of a cavity to be carried out and enables the volume of calculations in the numerical modelling to be reduced when taking account of additional factors.