SECONDARY PRESSURE WAVES 383 



bubble migrations and secondary pulse pressures are subject to some 

 scatter because of the various errors enumerated, there is considerable 

 evidence from these and other measurements that several aspects of the 

 phenomena are not very reproducible under presumably identical con- 

 ditions. For example, bubble pulse pressure-time curves on successive 

 shots often show distinct qualitative differences in their general outline 

 and occasionally exhibit one or more sharp narrow "spikes" of fairly 

 large amplitude superimposed on the profile. This latter feature is 

 plausibly explained by the hypothesis of collapse of local pockets of gas 

 or other distortions formed on the contracting surface. This explana- 

 tion is consistent with the observation that the spikes and other ir- 

 regularities are more frequently observed for the hydrodynamically less 

 stable condition of rapid vertical motion near the minimum. It is also 

 in accord with the result that indicated positions of the sources of dif- 

 ferent spikes on a given record obtained by sound ranging measure- 

 ments often disagree, sometimes by amounts comparable with the mini- 

 mum radius of the bubble. 



Comparison of pressure and migration results show that the scatter 

 is generally much greater in measurements near the surface or bottom. 

 As mentioned in section 8.11, these variations are not surprising in view 

 of the sensitiveness of motion near the minimum to the exact condi- 

 tions, such as surface waves and irregularities of the bottom. Wilhs 

 and Ackroyd (122) have commented on evidence of lack of reproducibil- 

 ity of secondary pressures, particularly when the charge is fired on or 

 near the bottom, weak and irregular pressures being observed. The 

 conclusion that the motion during the short interval near the time of 

 minimum radius is most critically affected by shght differences in ex- 

 perimental conditions is easily understood from the hydrodynamics of 

 the motion. It is also supported by the fact that period and maximum 

 radius measurements, which are quite insensitive to changes in this time, 

 show very much less scatter. Period measurements, for example, are 

 rather easily reproduced to plus or minus one per cent, and the chief 

 uncertainty is selection of the time of minimum radius on the pressure- 

 time record. 



It is reasonable to conclude that the extreme precautions which are 

 necessary to achieve much greater precision in experimental methods 

 would be for many purposes unwarranted, owing to variations likely to 

 be inherent in the phenomenon under many conditions and the rather 

 approximate nature of theories so far developed. 



9.6. Experimental Measurements of Secondary Pulse Pressures 



A. Stnall charge results. It is to be expected that experimental 

 pressure-time curves for bubble pulses will be in better agreement with 

 theoretical predictions in the case of small charges. This is because the 



