Nonlinear Effects in the Collapse of a Nearly Spherical Cavity in a Liquid

Abstract : A linearized perturbation theory was developed some time ago for the analysis of the growth of distortions in a nearly spherical cavity collapsing in a liquid. Since the distortions grow as the cavity collapses, it is of importance to determine the validity of the linearized approximation. The study gives a numerical solution of the exact nonlinear equations for the growth of a distortion. Two kinds of distortions are studied in detail: Case A is essentially a prolate ellipsoid; Case B is essentially an oblique ellipsoid. Both cases have initial large deformations from the spherical shape. The numerical solution shows that the linearized perturbation approximation remains surprisingly accurate through most of the cavity collapse. The principal effect of the nonlinear calculation is in the coupling of the various distortion modes.