that friction effects are negligible, or of second order in . 
importance, in the problem of wave forecasting. 
Transformation of sea into swell 
The results of Chapter 8 and of this chapter also explain 
all of the known effects which accompany the transformation of 
sea into swell. Short crested waves are simply sums of waves with 
infinitely long crests such as equation (8.5). A short crested 
Gaussian sea surface is given by an integral of the form of equa- 
tion (9.47). The greater the variation of [An(p ,0)]° over / and 
@ the more irregular, choppy, and short crested the sea surface 
will be at the source. The apparent crests will actually vary in 
direction depending upon what particular terms happen by chance 
to reinforce at a particular time and place. For example, if 
[en 0) 1 were given by, say, figure 22, and if a partial sum 
such as equation (9.48) were formed over a net containing about 
fifty elemental net areas, the resulting equation for 7 (x,y,t) 
would represent a very complex irregular short crested sea surface 
which would approximate (even for such a coarse net) many of the 
features of waves at the edge of a storm at sea. 
Now consider the power spectrum given by applying filter V 
to figure 22. For any partial sum, all the elemental waves would 
be traveling in directions only a few degrees from -22.5° and all 
the elemental waves would have nearly the same spectral periods. 
The sea surface would therefore have to consist of large areas 
of waves of nearly uniform height with quite long crests all 
traveling in the same apparent direction. Arguments similar to 
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