section of speech, although in reality the frequencies are slowly 
varying (compared to the duration of one cycle), can be treated 
this way without any serious consequences. 
Consequently, the results of this chapter will apply to 
almost any wave situation. If there is reason to believe that 
the waves are changing very, very rapidly, the results of the 
analysis should be questioned, but for slowly varying situations 
the results can be interpreted in the light of the theoretical 
considerations given in the previous chapters. 
For these reasons, [a(n 1° and [a,(# ,e)]° will represent 
power spectra for any sea surface either at the edge of a storm 
or in the area of decay. No special notation will be used to desig- 
nate special conditions. 
Non-Gaussian short crested sea surfaces 
Consider, for example, the short crested sea surface given 
by equation (8.1). For this representation of the sea surface, 
it is possible to pick some fixed point on the sea surface, say 
xy and Yu and observe the wave system at that point as a function 
of time. ividently, there will be places at which very small 
(or zero) amplitudes will be observed, and at other places the 
amplituces will be quite large. 
In equation (10.1), the potential energy averaged over time 
at the point (x5 9 ¥z) is computed. The result shows that the value 
t is 
obtained is still a function of Yy° At some points, P.E. 
pean /4; at others, P.E." is zero. The potential energy averaged 
over y and t is peA-/8. (See also equation (8.5).) 
At first, the point just made above does not appear to be 
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