NONLINEAR OSCILLATION OF A GAS-FILLED SPHERICAL CAVITY IN AN INCOMPRESSIBLE FLUID

A classical problem in bubble dynamics, whose study was originated by Rayleigh, is reconsidered. The nonlinear free oscillation of a spherical bubble is analyzed in detail, the bubble consisting of a gas obedient to the polytropic law and surrounded by an incompressible inviscid liquid. Firstly, it is shown that the process of bubble collapse may be classified into three distinct stages, according to the pressure distribution in the liquid, while only two stages exist in the collapse of a vacuum cavity. It is also shown that the solution of the non-linear oscillation of the bubble can exactly be represented in term, of Weierstrass elliptic and related functions if the polytropic exponent of the gas is equal to 4/3, i.e . that of vapour.