261^. SHOCK WAVE MEASUREMENTS 



wliich arrives at the time for a direct wave from the charge, is preceded 

 by a gradually rising pressure reaching a value of about 40 per cent of 

 the shock discontinuity when the latter arrives. 



The initial gradual rise in pressure must be the result of a disturb- 

 ance which is propagated in the bottom material at higher velocity than 

 in the water. Refraction, or possibly diffraction, of this kind implies 

 an inhomogeneity of the bottom, as otherwise the transmitted wave in 

 the bottom would travel in a straight line, and none of its energy would 

 be returned to the w^ater above it. A somewhat different mechanism, 

 which is known to play an important part in long range transmission of 

 sound, is the generation of seismic or earthquake waves which in turn 

 generate waves in the adjacent water. Usually, but not always, a bot- 

 tom reflection corresponding in time to the geometrical reflection path, 

 and of rather smaller amplitude than computed for a rigid bottom, is 

 observed for charges fired near the bottom. The time and magnitude 

 of the ground shock depend on the nature of the bottom, and also vary 

 considerably with the relative positions of the charge and point of obser- 

 vation with respect to the bottom. The character of bottom effects is 

 thus not simply described, and their study is of more value in an under- 

 standing of the bottom structure than of the shock wave in water. 



C. Other boundaries. The study of effects near homogeneous walls 

 and targets should at least give more straightforward results than reflec- 

 tions off the sea bottom. Unless such boundaries are rigid and of large 

 extent compared to the length of the shock wave, however, complications 

 arise in these cases also. For example, a yielding structure may at 

 first act as a rigid surface because of its inertia, but at later times when 

 it has been set in motion, it acts more as a free surface. If in addition, 

 the least dimension of such a surface is not large compared with the 

 shock wave, the propagation of the shock wave is no longer simply de- 

 scribed by simple reflections, and diffraction waves are established in 

 the vicinity of the structure. The description and analysis of what 

 happens in such cases is evidently as much a function of the structure 

 as of the underwater pressures. Detailed discussions of problems of 

 this kind are far beyond the scope of this book, but some general con- 

 siderations are indicated in section 10.6. 



7.9. The Shock Wave at Large Distances 



As shock waves are propagated outward from an explosive source 

 they become weakened by both dissipation and divergence. One might 

 then expect that the characteristic features of finite amplitude waves 

 would disappear rather rapidly, leaving a wave propagated essentially 

 according to the acoustic approximation. The propagation theory of 

 Kirkwood and Bethe indicates, however, that even at large distances 

 from the charge the peak pressure falls off somewhat more rapidly than 



