Ex-ptosion-Generated Water Waves 



4,4 Energy Coupling 



The deficiencies of simple exponential scaling are more appar- 

 ent when considering the efficiency of energy coupling into water 

 waves. The analytic source models discussed above are linear, and 

 thus the total wave energy is equal to the potential energy of the 

 source model; i.e. , proportional to 'HoR^. But, in view of Eq. (26), 

 the empirical relations given in Eq. (27) imply that ti^rZ ~ w'°®, 

 which obviously cannot be true for all yields, since it states that 

 wave energy increases faster than explosion energy under geometri- 

 cally similar conditions. It is also pertinent to recall that the calcu- 

 lating of energy based on the theoretical source model may lead to a 

 significant error; since only the first wave train has been watched 

 with experiments, it may happen that the following wave train contains 

 less energy than the theoretical model, as due the dissipative 

 mechanism which influences the high frequency waves. Keeping in 

 mind these reservations, it is found that the energy in the wave train 

 is 



E^ = 126 (ti r)^ ft-lb. 

 W ^ 'max ' 



Then, inserting the value of "Hf^ax^ ^^ terms of yield and water depth, 

 it is found that at lower critical depth, the efficiency e is 



e = 0.0074 W°°'^= i% (W is in pounds). 



At upper critical depth, the increase of efficiency with yield 

 within the range of available experiments is even more pronounced. 

 For example, e which is 1% in the case of 0,5 lbs of TNT has been 

 found to be 6% in the case of an explosion of 375 pounds, which implies 

 that r]^ ~ W^O.ei g^^ upper critical depth. Such results cannot, of 

 course, be extrapolated to atomic yield. 



Since the fraction of yield energy appearing as waves is only 

 a few per cent for the largest tests so far conducted, we are faced 

 with the problem of trying to distinguish very small energy differ- 

 ences in normalizing analytic models to actual experiments. While 

 the present models provide adequate predictions for the largest 

 waves over an Impressive range of yields (0,5 - 64,000,000 lbs TNT 

 equivalent). It Is recognized that important phenomenological factors, 

 such as atmospheric pressure, shock Interaction, and cavity stability 

 have been neglected, each of which can reasonably be expected to 

 Influence wave formation to some extent. What Is really surprising 

 is that such simple models work as well as they do, considering the 

 great complexity of the process of explosive wave generation. 



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