Imag 



CAVITATED REGION 



Depth-Scale lOx Length Scale 

 (feet) 



300 200 



100 



100 



I / 



Y 



Pressure- Time Curves 

 for Point P 



0. 5 lb Charge 



_ 10 



. 20 



40 



Figure 4. Reflection of a shockwove from the water surface. 



calculate the fluid motion within such a cavitated region or to understand when and 

 how the closure of this cavitation occurs. 



The acoustic approximation seems to describe the surface effect reasonably 

 well. But, if we give the problem a closer look, we find again that we are dealing 

 with high amplitude waves and that the acoustic approximation can be misleading. The 

 first evidence is seen in Fig. 4 and it is inconspicuous enough to be overlooked. The 

 surface signal arrives earlier than calculated by the acoustic theory, also there is not 

 a clean cut-off, — but a gradual decrease of pressure. Obviously this faster-than-acoustic- 

 propagation is a finite amplitude effect. This fore-running of the surface signal be- 

 comes more and more pronounced the shallower the point of observation is, Fig. 5. 

 Finally, the surface signal arrives so early that it reaches the shockfront itself. This 

 point lies on the boundary of the anamolous surface reflection (Penny and Keil [11]). 

 Beyond this point the rarefaction from the surface engulfs the whole wave and changes 

 drastically the profile of the wave. Rosenbaum and Snay [12] have treated this 

 problem theoretically by using the approach of the pseudo-stationary fluid motion. 

 The agreement of these calculations with experimental evidence is good. However, 

 we do not have a precise mathematical description of this phenomenon yet. 



Bubble Phenomena 

 The Migrating Gas Bubble 



Fig. 6 shows a migrating pulsating bubble. The pictures are from a model test 

 where the air pressure above the water surface was reduced. By this way it is possible 

 to scale the effects of gravity and to simulate realistically the bubble migration. By 

 adjusting the air pressure to a certain value, it is possible to scale any desired charge 

 weight. For instance, this test corresponds to a 354 lb. TNT charge detonated in a 

 depth of 80.8 feet. 



The change of the shape of the bubble is interesting. At the moment of the 

 maximum expansion the bubble is an almost perfect sphere. But, when the bubble con- 



331 



