Explosion-Generated Water Waves 



^(r,t) = ^^ ( -dVVdk ) -^B^^R) ^°s (kr - tVk tanh k) , (22) 



the two "cavity parameters" -n^ and R being embodied within our 

 previous expression for the envelope amplitude, A. It is through 

 empirical determination of these two parameters that we hope to 

 correlate theory and experiment. 



4. 2 Experimental Correlation 



While tIq and R cannot be experimentally measured, they 



can be determined indirectly from k„^„ and ^^^jr , which are 



' max 'max ' 



characteristic of the source disturbance, and also ineasurable. 

 Hence, we seek to relate ^^Qy^ and 'Hmax-'' to the characteristics of 

 the explosion by experiment , and r\^ and R to ^^ox ^^'^ ^ma>F 

 by theory . The expression giving k^^^ in terms of y]^ and R is 



dA 



dk 



= (23) 



since this expression defines the maxima of the wave envelope; the 

 least non-zero value of k for which the above expression holds is 

 k_... 



and 



For k > 3 (relatively deep water), ~Tv7dk ~ v2 = const, 



/2"iloR 



f^ J (kR) . (24) 



r 3 



Therefore, k^^^ can be determined from the first turning value of 

 the Bessel function J (kR); viz for 



k^^ = 4.20. (25) 



Our other measurable, "Hmax^ ' "^ay now be related to r\Q and 

 R by evaluating A^^^ (or "Hmax) at k = ^matr When this is done and 

 the resulting expression is sinnplified, we have 



tIqR = 1.63Ti„axr . (26) 



All that remains now is to relate flmax^ ^^^ ^max ^° ^^^ 

 characteristics of the explosion; these are W, explosive yield in 

 pounds of TNT, Z, detonation depth in feet, and D, the water depth 



85 



