Explosion-Generated Water Waves 



Figure 6 presents examples of the matching between theoreti- 

 cal wave envelope and wave records due to a 9. 620 lb TNT explosion. 

 The slight irregularities in the symmetry of the recorded wave trains 

 are attributed to partial shoreline reflection interferring with the 

 radiating wave trains (Hwang et al. [ 1969] . But, in general, the 

 computed wave envelopes agree fairly closely with the observed 

 amplitudes. 



4. 3 Limitiations of the Model Due to Scale Effects 



An examination of Fig. 5 reveals that the bulk of data upon 

 which predictions are based are restricted to yields from one-half to 

 a few hundred pounds of TNT. One wonders then just how reliable 

 extrapolation to very large yield (say, lO'^ pounds of TNT) would be. 

 The limited data available from nuclear explosions is insufficient to 

 resolve this problem. Comparison between crater data in soft 

 materials for both nuclear and TNT explosions suggest that the laws 

 of similitude nnay be applied to contained explosions but may not 

 apply over a large yield range for venting detonations. In particular, 

 the shock wave from a nuclear explosion travels much faster in air 

 than in water, which is not the case for a TNT explosion. 



We may infer several things, however, just from t]ie nature 

 of the scaling parameters given by Eq. (27). Consider, for exannple , 

 the groups ^ max^*/^°^^ ^^^ Z/W°-^. In each, the exponent of W 

 was chosen to best compress the data of Fig, 5 into a single curve, 

 since W represents an energy, dimensional analysis suggests that 

 ^max^/^^/PS)''^^ ^^^ Z/(W/pg)'/'* are appropriate scaling parameters, 

 although similar conditions also require that other parameters, such 

 as atmospheric pressure and sonic velocity in water, should also be 

 scaled with yield. These conditions are never satisfied experimental- 

 ly, and it is therefore not surprising that exponential scaling alone is 

 not satisfactory. Moreover, the fact that the parametric coefficients 

 vary with Z means that the phenomena are not simply scalable 

 (Pace et al. [ 1969]). Lastly, the lack of evidence for an u. c.d. at 

 large yields suggests that the generation process is fundamentally 

 different. 



For small yields (and subsequent small depth at burst) hydro- 

 static pressure is small compared to atmospheric pressure; for 

 large yields the reverse is true. In the former extreme, dimensional 

 analysis suggests 1 /3 power scaling; in the latter, l/4 power scaling. 

 In an analogous review of earth crater scaling, (Chabal [ 1965]) has 

 proposed an "overburden scaling law" in which the scaling exponent 

 varies between these two extrenties, but without convincing improve- 

 ment in agreement to the experimental data. 



87 



