to a constant value in the storm for the duration of the waves and 
then died out smoothly to zero again would be the most practical 
one to start with. 
Fp (t,4) = (1/r)[tan*(t/B,) - tan*(t - Ds + F/B] 
might be quite a practical one. The parameters, By and Bo» could 
be related to the build up time of the waves. As the two values 
of B approach zero, Fe (t) becomes in the limit equation (7.51). 
Such a representation would probably eliminate the Fresnel fringes. 
Physical interpretation of the forecast diagrams 
The waves at the source can be characterized as "sea." The 
waves at large x can be shown to have the properties of "swell." 
One of the ways in which the apparent period of ocean swell can 
increase with travel time is explained by this model. The analy- 
sis, however, is still incomplete because it does not contain any 
of the properties of short crested waves. 
At the source, the power spectrum might look like the one 
assumed in figure 15. There is some indirect evidence which sup- 
ports this general shape. The partial sum given by equation (7.32) 
shows that the sea surface can be represented by the sum of many 
vectors in the complex plane. These vectors have many different 
angular speeds. Suppose that at some instant of time, some numbe1 
of the vectors add together to give a definite peak amplitude to 
the projection of the sum onto the real axis. And also suppose, 
aS indeed must be the case, that the other vectors all add together 
to very nearly zero. These vectors which add to give the displace- 
ment are all rotating at widely different values of uw . Hence 
after they have gone around the circle several times they will 
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