The period of the first pulsation [1] is more than one half second for common 

 charges. This is a long time when compared with the extremely fast processes occurring 

 with explosions. In particular, this duration is long enough for gravity to become 

 effective. Such a bubble has great buoyancy and, therefore, migrates upward. How- 

 ever, it does not float up like a balloon, but shoots up in jumps. 



In Fig. 1, the dotted curve represents the position of the bubble center as a 

 function of time. This curve shows that the rate of rise is largest when the bubble is 

 near its minimum, but is almost zero when the bubble is large. (Note that Fig. 1 is a 

 time plot of bubble position and size. It must not be interpreted that the bubble moves 

 sidewards. Actually, the bubble rises vertically upward.) 



The interaction of the pressure waves and the pulsating bubble with the water 

 surface, the bottom of the sea and the target structures produces a great variety of 

 interesting phenomena and effects. Some of these will be discussed in this paper. 



Shockwave Phenomena 



Shockwave Formation 



Fig. 2 illustrates the formation of the Shockwave by a detonating charge. The 

 graph shows the pressure-distance distribution at two moments t 1 and t 2 . We assume 

 a spherical charge which is ignited at the center. A spherical detonation wave proceeds 

 outward causing the reaction of the explosive in concentric shells one after the other. 

 At the moment t = t 1 this detonation wave has reached the charge surface and the 

 explosion is completed. The graph shows the pressure distribution inside of the gas 

 globe for this instant, curve labeled t ± . The maximum pressure occurs at the surface 

 of the gas globe. The pressure-distance curve decreases rapidly — in fact, discontinuously 

 — at this point when going toward the center. Proceeding further in this direction, the 

 pressure levels off and becomes constant at a distance of about one-half of the radius 

 from the center of the gas sphere. The infinitely sharp pressure spike at the surface 

 of the gas sphere is a consequence of the spherical propagation of detonation waves (G. 

 I. Taylor, Doering [2]). 



The pressure transmission from such a high pressure gas ball to the ambient 

 medium has been calculated by Wecken [3] as well as Holt and Berry [3]. They have 

 studied the problem of a detonating charge in air. Fig. 2 shows an adaptation of their 

 results to an explosion in water, curve labeled t 2 . The gas globe has expanded as 

 indicated by the dashed circle. Ahead of the bubble the Shockwave has moved into 

 the water and a rarefaction wave runs back into the gas. There is a small second 

 shock which propagates toward the center. At a later moment this shock will be 

 reflected at the center and will be finally transmitted into the water. Experimentally 

 observed Shockwaves show a small but reproducible irregularity in their tails. It is 

 believed that this caused by the "second shock." 



When the maximum Shockwave pressure is traced back to the gas globe, one 

 finds that the initial Shockwave pressure in water is about one-half of the detonation 

 pressure. This means the gas expands only partially when the Shockwave is formed 

 and only a fraction of the total energy of detonation is transmitted into the shock- 

 wave; the remainder produces the expansion of the gas globe and the bubble pulsations. 

 It turns out [4] that about 50% of the total energy is radiated in the Shockwave and 

 that the other 50% constitutes the bubble energy. 



Although the problem of the Shockwave formation by a detonating charge is 

 basically understood, no numerical calculations applicable to underwater explosions 

 have been made so far. The same holds for the subsequent propagation of the high- 

 amplitude Shockwave through the water. It might be mentioned that there are several 

 approximate treatments (Kirkwood-Bethe, Kirkwood-Brinkley, Snay-Mathias [5]) which 

 describe these phenomena accurately enough for many practical purposes. However, 



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