MOTION OF THE GAS SPHERE 



271 



The maximum velocity of the bubble surface as the bubble ap- 

 proaches minimum radius is about 200 ft. /sec. in the example and over 

 most of the motion is very much less. The maximum radius of 1.48 

 feet corresponds to an internal gas pressure very much less than hydro- 

 static (roughly one-fifth), as the equilibrium radius for this size charge 

 is readily estimated to be 1.0 feet. This radius, for which the gas is at 

 the hydrostatic pressure of the water, is indicated by the dashed line in 

 Fig. 8.1 and it is evident that the pressure is less than this over some 80 

 per cent of the first cycle. The length and time scales will of course 

 change with the size of charge and the depth at which it is fired, being 

 larger for larger charges and shallower depths. In general, however, it 



20 



40 

 TIME (msec) 



60 



80 



Fig. 8.1 



Radius of the gas sphere as a function of time, for a 0.55 pound 

 tetryl charge 300 feet below the surface. 



is true that the radial velocities will be of the same order of magnitude, 

 and that over most of the cycle the pressures are much smaller than 

 hydrostatic. 



These conclusions about the bubble motion are the basis of all the 

 bubble theories which lead to general numerical predictions of bubble 

 radius, migration and period. It is a common characteristic of such 

 theories that changes in density of the water surrounding the bubble 

 are neglected (the noncompressive approximation) and it is further as- 

 sumed that the bubble retains a spherical form throughout the motion. 

 From what has been said, it is evident that both these assumptions are 

 at least plausible as far as the expanded phase of the motion is con- 

 cerned. They must, however, be increasingly poor as the bubble ap- 

 proaches its minimum radius for which very much larger pressures and 

 acceleration are involved. At this radius, for example, pressure waves 



