Oscillations of the Gas Bubble Produced by an Underwater Explosion.

In this report it is shown that the gas bubble resulting from an underwater explosion would experience undamped pulsations under the assumptions that the products of the explosion behave as an ideal gas and undergo adiabatic changes, and that the water about the bubble is an infinite medium which undergoes incompressive spherical flow. A method is given for determining the minimum radius corresponding to an experimentally measured maximum value of the radius and a given value of the gas constant gamma. Three separate methods are presented by means of which an integral solution of the differential equation governing the phenomenon can be written. Variations in the radius-time curve due to alterations in gamma are also discussed. In particular, it is proved that neglecting the potential energy of the gas bubble leads to the same radius-time curve as that obtained by letting gamma become infinite and that this curve most nearly approximates the experimental data, over the contraction phase of the first cycle, provided the above assumptions are fulfilled.