WATER SURFACE 



CHARGE 



O 



PRESSURE- TIME HISTORIES 

 AT VARIOUS DEPTHS 



Figure 5. Anomalous surface reflection. The pressure-time curves refer to the points indicated by the 

 arrows. The dashed curves show the shape of the wave from acoustic treatment. 



tracts, the sphere is distorted. The straight bottom seen on the second frame is due to 

 the fact that the bubble surface is inverted into the inside. The actual lower bubble sur- 

 face is faintly visible in the interior of the bubble. 



This change of shape is caused by the difference of the hydrostatic pressure 

 between bubble top and bottom. Therefore, upon contracting, the bottom of the 

 bubble is pushed inward faster than the top and the kidney-like shape seen in the 

 second frame of Fig. 6 is formed. A short instant later the two interfaces impinge on 

 each other and the bubble becomes a torus (third frame). The gas is near the periphery 

 and there is water all the way through the bubble near the center line. As in a vortex 

 ring there is a strong upward velocity near the centerline and this carries the bubble 

 upward when it re-expands. 



The last frame shows the moment of the second bubble maximum. The bubble 

 is almost spherical again. The black region below the bubble is water which is 

 darkened by the solid products of the explosion. 



The inversion of the bubble is apparently the mechanism by which such a 

 migrating bubble dissipates its translational energy or in other words it is the mechanism 

 by which the drag of such a moving bubble is originated. The analogy to the re-entrant 

 jet of fast moving bodies under water is apparent. This impinging of the two inter- 

 faces produces a water-hammer effect and dissipates energy. It also introduces vorticity 

 into the sofar irrotational fluid motion. 



Kolodner and Keller [13] and, earlier, Penny and Price [1] have attacked the 

 problem of the bubble contraction in a gravitational field and carried the calculations 

 to a point shortly before the collision of the interfaces. These calculations describe 

 the change of shape very well. No attempt has been made so far to follow up the 

 later phases, for instance to treat the bubble as an expanding vortex ring. 



The Bubble Pulse 



Fig. 7 shows the pressure-time record of a bubble pulse. This record has been 

 obtained from a 1600 lb. TNT charge exploded at a depth of 100 ft. In this case, 



332 



