and 



Le Mehaute 



F = (G^ - G^,r))^._Q Zo=z = (6) 



Q 



Jq tT 



= - V Pr<^Tt dT + (pG^t)T=0 Zq = z = (7) 



Jo 



It can be seen that F| contains the contribution to r| from 

 the initial velocity and surface deformation of the source while F2 

 represents the influence of initial pressure. Therefore, the model 

 is very general; in fact, Kajlura [ 1963] gives an additional term repre- 

 senting the contribution from an arbitrary bottom disturbance, which 

 is ignored here. It has been found, however, that such generality is 

 not necessary in order to make practical predictions of water wave 

 production. Instead, it is possible, for example, to absorb the 

 effects of initial velocity and pressure into a fictitious initial surface 

 deformation, chosen in such a way that the predicted waves are 

 essentially the same as would be found using actual velocity, defor- 

 mation and pressure. 



3. 2 Simplified Approach 



The advantage of this approach in practical work will be 

 apparent later in discussing the correlation between theory and 

 experiment. The essential point, however, is that, instead of 

 needing to predict the complicated phenomena leading to initial 

 deformation, velocity and pressure, it may be sufficient to utilize 

 easily measurable quantities to calibrate a simplified source model. 



With this in mind, we rewrite Eq, (5) as a Green's function 

 of time only: 



^=^yy (- G,t^)r=odSo ^0 = ^ = (8) 



S 



Furthermore, it is reasonable to assume that, for a single 

 explosion in water of constant depth, the problem is symmetric about 

 the z-axis passing through the source. When the appropriate opera- 

 tions [ in Eq. (8)] are performed, and the transformation to cylindri- 

 cal coordinates (r,0) is made, one obtains the time-and- space 

 dependent surface elevatior 



78 



