nature of the sea surface in the storm. 
Example one is a possible form for E,(#,6). The  ,© polar 
coordinate system is broken up into five areas as shown in the 
little sketch on the side of the plate. In area A, the value of 
E,( 48) is constant and equal to the values given in equation 
(9.49). The figure is cut off at finite values of ” , but the 
same value holds for © between 7/4 and 1/2 and # greater than 
27/5. In the other areas, the values of E,(u,@) are given by 
the appropriate functions in equation (9.49). Note that E,(p ,0) 
is continuous. 
Area D is the only area in which E5(p 40) is a function of 
both 6 andw. The second mixed partial derivative is different 
from zero only in this area. [a,(p ,0)]1° is equal to K* in this 
area, and it is zero everywhere else. For any partial sum, with 
a small enough net, there would be no component wave crests travel- 
ing in directions between -m/2 and -17/4, and in directions between 
t/4 and 1r/2, and there would be no component wave crests with 
periods greater than 10 seconds or less than 5 seconds. In the 
limit, if the phases were random, the wave system would still be 
Gaussian. 
In equations (9.49) and (9.50), if K* equals 1.69 10? em 
sec, then E equals 2.5 10? om’. The potential energy in the 
2max 
system averaged over y and t is then equal to 6.25 10” ergs/em- 
(if the product pg equals 103 em/cm*sec“). 
Example one is physically not a very realistic example. It 
would not be expected that a turbulent process such as the one 
which produces waves in a storm at sea could produce such a sharp 
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