DISCUSSION 

 G. Chertock 



I think that Dr. Snay has given us a very interesting survey of the hydro- 

 dynamics of underwater explosions. I am particularly impressed by how well he man- 

 aged to avoid all the confidential and classified material. That is quite a difficult job. 



I noticed a couple of points that were new to me, but were very interesting. 

 One was the reason why the low shock wave pressures do not match the same curves 

 as the high shock wave pressures. 



This is something that we have known for some time, but I was interested in 

 his suggestion that this may be an instrument effect, and I think we will look into it 

 ourselves. 



I was also interested in the photograph that we saw of the bubble welling up 

 and not forming plumes — it just seemed to come up as a lazy ball, with water spilling 

 around it. As Dr. Snay remarked, this is probably due to a bubble rising without 

 pulsating. This is important to our work, because the pressures that are due to such 

 a bubble are largely due to the pulsations. A nonpulsating bubble would have a very 

 different pressure field, and a very different damage potential. 



At the Model Basin most of our work has been in the interaction of the pressure 

 wave with structures. The most difficult problems have not been the hydrodynamics but 

 rather techniques for handling the structural reactions. 



For example, Dr. Snay mentioned three cases of structural response. One of 

 them is the deformation of a diaphragm. We don't know how to treat the mechanics 

 of the diaphragm too well. The diaphragm material is expanding under some yield 

 stress which is a function of the strain rates, and yielding is often delayed because of the 

 delay time we know so little about. And the whole problem is nonlinear. In fact, 

 there are so many parameters that you are often free to pick and choose, and make it 

 fit any theory you want. 



The second thing he discussed was the reaction of the infinite cylinder to a 

 shock wave. You may have noticed the fact that the shock wave he took was a plane 

 shock wave. In practice, of course, it almost always results from the point charge and 

 we have a spherically divergent wave. We have difficulty treating that problem with 

 any precision. 



The third problem he mentioned is the whipping problem. There we made 

 quite a few measurements on highly idealized models and we have had very good 

 success in comparing the measurements with theoretical predictions, but it was models 

 where we have knowledge of the structural characteristics of the model. 



S. G. Reed 



I hope it will not be an undue distortion to expand a bit on one or two points 

 out of the wealth of interesting material presented by Dr. Snay. 



Dr. Snay mentioned briefly the Bjerknes fields when talking about the attraction 

 or repulsion of the explosion bubble near surfaces. The early discussion of Bjerknes 

 is very suggestive ... at least to one interested in the physics of the phenomena. I 

 would like to give an example. 



There is an analogy to electrostatics which has been used by Dr. Kennard and 

 others in connection with the attraction or repulsion: the pulsating bubble far from 

 surfaces can be replaced in first order by a "charge" Q proportional to the rate of 

 change of its volume: 



1 dv 



Q = 



4x dt 



The analogy is that the forces between pulsating volumes are proportional, to 

 first order, to the product of their respective charges, but with sign reversed to the 



347 



