low local chop power spectrum, then the methods of analysis pre- 
sented in Chapter 10 will separate the two spectra. 
Some properties of the refraction of short crested Gaussian waves 
Consider the refraction of the most elementary short crested 
wave system possible as given by equation (8.1) or by equation (8.4). 
Let the angle in deep water between the two elemental crests be 
given by, say, thirty degrees. Given the discrete spectral period, 
it is then possible to find the apparent length of the crests in 
the direction of the crests in deep water. 
If the system is approaching an uncomplicated coastline without 
crossed orthogonals for that discrete spectral component and without 
caustics, then the closer to the shore the system is studied, the 
more the angle between the elemental crests is decreased because the 
crests are more nearly parallel to the shore. Thus nearer shore the 
apparent crests are longer than they are in deep water. 
For any power spectrum with discrete spectral components such 
as the one treated in equation (8.5), the same thing occurs, and, 
in the limit, for the continuous power spectrum the same results are 
accounted for by 9( 4,0.) and [(p ,O,). 
If in addition, the power spectrum varies over a wide range of 
HM, the low # valiues are amplified in general more than the high 
values of # by the effect of the factor, D, in wave refraction 
theory. Consequently, as a short crested sea surface approaches a 
coast in many cases, the crests become longer and more well defined, 
and the "significant" period of a wave record near the shore becomes 
longer than the "significant" period of a record taken at the same 
time in deep water. The refraction of a short crested sea surface by 
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