8. Motion of the Gas Sphere 



8.1. General Features of the Motion 



After emission of the shock wave, the gaseous products of an explo- 

 sion continue to expand outward at a gradually decreasing rate. As a 

 result there are considerable radial displacements of the water, but the 

 changes in velocity take place at a much slower rate than in the initial 

 phases of the motion immediately following detonation. The pressures 

 in the surrounding liquid are therefore much smaller and the whole 

 character of the motion changes. Although the same basic hydro- 

 dynamical equations apply as in the case of the shock wave, and exact 

 solutions would be at least as difficult to obtain, the qualitative dif- 

 ferences in the later motion make more appropriate somewhat different 

 approximations. In order to see the reasons for these and their limi- 

 tations, it is helpful to examine briefly some experimental studies of the 

 motion before considering the various theoretical developments. 



A series of frames from a motion picture record of bubble motion 

 (105) is shown in Plate IX; the charge used was 0.55 pound of tetryl 

 detonated 300 feet below the surface of the water. The time intervals 

 between these frames are all nearly equal, as indicated, and it is evi- 

 dent that an initial rapid expansion of the spherical bubble is gradually 

 brought to a stop after 0.014 sec. The bubble^ then contracts at an 

 increasingly rapid rate until it reaches a minimum 0.028 sec. later, and 

 after an abrupt reversal again expands. Throughout the expanded 

 phase of the bubble's motion there is very little vertical migration but 

 near the minimum radius an appreciable upward displacement occurs. 

 The reversal of the bubble motion at the minimum occurs so abruptly 

 as to be virtually discontinuous on a time scale suitable for the rest of 

 the motion; this characteristic is shown clearly in Fig. 8.1 in which the 

 bubble radius is plotted as a function of time. A further qualitative 

 feature of significance is the fact that the bubble retains its identity at 

 the minimum despite the large radial accelerations and appreciable 

 vertical motion, and remains fairly symmetrical. The motion is, there- 

 fore, a reasonably stable one in fact. A further evidence of overall 

 stability is the continued oscillations of the bubble (if the charge is fired 

 sufficiently deep to permit them to occur before the bubble rises to the 

 surface) : three or four complete cycles are readily observed and at least 

 ten such cycles have been shown to exist for very deep charges. 



^ In the discussion of this and the next chapter, the gas products from an ex- 

 plosion are frequently described by the term "bubble" in common usage, although 

 the term "globe" emi)loyed in Taylor Model Basin reports avoids possible con- 

 fusion with other kinds of bubble. 



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