331 



presented here explains these effects and gives a quanti- 

 tative estimate of their sl25e. The values predicted for 

 the period show excellent agreement with those obtained 

 experimentally, while the values predicted for the peak 

 pressure and the distance moved by the bubble show only 

 fair agreement. 



An important application of the theory is the deter- 

 mination of the amount of energy left in the bubble after 

 the shock wave has passed. Also the energy in successive 

 bubble oscillations can be foxond. There is a large amount 

 of energy dissipated in the transition from shock wave 

 stage to bubble motion and also between successive bubble 

 oscillations, which cannot be explained on the basis of 

 the energy radiated by the pressxire pulse. The explana- 

 tion of this large energy dissipation is still unknown. 



Outline 



As developed in this paper the theory is an exten- 

 sion of that given in AIJP Report 37. IR, studies on the 

 Gas Bubble Resulting from Underwater Explosions ; On the 

 Best Location of a Mine Near the Sea Bed . There, the 

 motion of the bubble in the presence of a rigid bottom 

 was investigated and it was shown that the exact theory 

 could be successfully approximated by the addition of a 

 term to the kinetic energy. In this paper we show that 

 the effects of surface, bottom, walls, targets, etc., can 

 all be approximated in the same way by the addition of a 

 suitable term to the kinetic energy. The evaluation of 

 this term depends upon the solution of an "electrostatic 

 problem." In Section IV we work out in detail the case 

 of a bubble between a free surface and a bottom. Other 

 cases can be treated in the same way. 



Section I presents a collection of formulas and a 

 svumnary of methods which can be used to predict the pe- 

 riod of oscillation of the bubble, the distance its 



