NSWC/WOL TR 76-155 



I. ON THE MOTION OF AN AIR BUBBLE SUBJECTED TO A SERIES OF STEP 

 CHANGES IN THE OUTSIDE WATER PRESSURE 



1. Consider a spherical bubble at rest in water at the 

 initial value p. of the ambient pressure. Let A± be its initial 

 radius when at rest. Its internal air pressure is the initial 

 ambient pressure p^ . At t = o, the ambient pressure jumps to a new 

 value p ; and the bubble is then oscillating. The situation for the 

 air pressure inside the bubble, trying to adjust to the new outside 

 pressure, is sketched in Figure A-l. 



2. In this Appendix we concern ourselves with the motion 

 of a bubble subjected to a succession of jumps to new ambient 

 pressures p n . At each ambient pressure the bubble motion is 

 described by the following differential equation J 



| (^A 3 ) A 2 +^P A 3 + E(A) = Y (Al) 



Kinetic Energy Potential 

 of Energy of 



Surrounding Water Pushed-back 



Water 



t 



Total Energy 



Internal Energy 

 of Air 

 Inside Bubble 



7. Cole, R. H. , 19U8, "Underwater Explosions", Princeton University Press. 



A- 2 



