Internal Waves tn Channels of Vartable Depth 
sity is uniform the motion is concentrated in a region near the free 
surface and the fluid does not ''feel'' the nonuniformity of the depth. 
But for internal waves, especially if the modes are high, that is to say 
if there are many internal zeros, then even for short waves the entire 
fluid participates in the motion, This has not been studied very much. 
My expansion scheme is not suitable at all for large wave numbers. 
One can do an asymptotic study of the differential equation to deal with 
that case, and I do not think it would be terribly difficult to do so. As 
to breaking, I should think that breaking is probably more severe for 
long waves. In fact, we know that long internal waves in a system of 
two layers indeed very often break, Although there are a lot of other 
solutions for non breaking waves (cnoidal waves, solitary waves and 
so on), if you make a laboratory test, pushing a plate against a layer- 
ed system you will see that indeed the interface breaks, Mathematical 
studies of the breaking of internal waves are even more difficult than 
the studies of the breaking of ordinary waves in one single fluid, and 
I certainly do not know the mathematical theory. You surely remem- 
ber the last picture shown by Pr. Plate. If a wave goes that far I 
would keep well away, both physically and intellectually. 
Secondly, about the interaction between surface waves and 
internal waves, that too has not been studied a great deal. We all 
know that after a storm there are internal waves created in the sea. 
How is the surface disturbance created and how are the messages 
transmitted from the surface down to the depths of the sea ? Notmuch 
is known about that. I think, however, that the interaction between 
surface waves and internal waves can be considered in this way : if 
the surface waves already created have a frequency very far away 
from that of any of the internal waves, there is no chance for the re- 
sonance phenomenon to happen. However, if short surface waves 
have the same frequency as some longer internal waves, the surface 
waves can excite internal waves, especially if the amplitude is not 
small, If the amplitude is small we do not need to worry about excit- 
ation, 
As for the effect of internal waves on moving structures, I 
do not have much to say about that. Naturally there would be an in- 
ternal-wave drag for moving’ submerged structures. 
The last question concerns the creation of internal waves by 
earthquake disturbances, I think that as far as the linear theory goes 
itis really just a matter of Fourier analysis. If one knows the details 
fo an earthquake, you can obtain the spectrum of internal waves creat- 
ed. Indeed, the linear theory should be quite simple. 
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