Impulsively Generated Waves Propagating into Shallow Water 



shallow water, and also that the boundary dissipation formula used 

 in the program does not provide sufficient attenuation. The assym- 

 metry of the envelopes show particularly good agreement and is one 

 of the strong features of the program. The observed trough levels 

 at stations 71 and 76 is slightly lower than predicted. This is 

 attributed to wave set-down due to the presence of a counterflow, or 

 backwash current. 



(b) For these two snaaller explosions the theory in general predicts 

 the correct number of waves in the envelope. Agreement in phase 



is poor at station 59 but better at subsequent stations. There is also 

 some grounds for suspicion of zero- set clock errors in the experi- 

 mental data so that it is difficult to make definitive statements on this 

 subject. The same suspicion makes it difficult to comment on the 

 agreement of the phase velocity of the observed waves. 



(c) The agreement in regard to the form of the waves in these 

 smaller explosions is especially impressive. The change from sinu- 

 soidal form to cnoidal form quite accurately represents the observed 

 waves , 



(d) The observed waves were nearly fully attenuated by the middle 

 of the second wave group. Stronger attenuation in the higher- 

 frequency range is required in the boundary dissipation formula, 



(e) Time of arrival (based on linear group velocity) of the wave 

 groups is in very good agreement indicating that transporting energy 

 at linear group velocity, even in the presence of noticeable viscous 

 effects, remains valid into quite shallow water, 



(f) The fit of the envelope for the large explosion, W = 0,224, at 

 station 59 is only fair. The observed envelope of the first group 

 reaches its maximum at a later time. It appears that for this source 

 strength the explosion may no longer be considered to occur in deep 

 water and that a different source model, perhaps one yielding a 

 higher-order Bessel function, is indicated. In addition the observed 

 troughs of the large waves were much lower than those predicted. 

 Again the probable cause is the presence of an observed strong back- 

 wash current which would have the effect of depressing the trough 

 level. The presence of backwash currents is not reflected by the 

 theory. 



(g) The agreement in phase is quite good at stations 59 and 64, but 

 not perfect. After wave breaking sets in the phase agreement de- 

 teriorates. One of the observed waves in the vicinity of the first 

 node decomposed into two component waves both of which eventually 

 broke. Otherwise, the theory predicted the correct number of waves. 



(h) For the large explosion breaking is predicted for the second wave 

 at station 64. Actually, the third and fourth waves broke at this 



259 



