72) = | | eho! O(@, w')dE(w)dE(w'), (9.6) 
and 
Q(w,w') = —[sgn(@), sent") (9.7) 
Then the spectrum of 7(t) was derived as 
co 
1 { [lm —Al(w —A) + AU]? 
=A) as (1g) — 2) g(1) 
sS(@)=S Orr 5 SM —A)s(A)dA 
-@ 
1 
= sV@) + sO). (9.8) 
s 
As an example, Tick took the simplified Neumann—Pierson type spectrum 
as sw) = 1.8 X 1.04w@~lw! > wo and computed this s@(w) for wo = 2,3,6 rad/sec. 
Figure 9.1 shows the results and (1/g*)s(w) is as small as several hundredths of 
s(q@) at the most. 
L. Tick® considered also a shallow water depth and derived the type of 
Q;(w,w') for this case that corresponds to Q(w,w’) in Eq. 9.6, as 
~~ LRRKE 06 w'—~=~6(w ty 
DG ON Sram ers Gin eine) aT 
(mn) 2 2 
ry2] RR 1 1, ok'+n'i¢@ _ (wr+o'y 
(w+@ ¥| BB Peano hte rena, 5) ee 
9. Sa 5 
(Ki k+1k'l k) tanh [d7(i k+1kl k')] - @Wt+o'y* 
Here d* =(h/g), k=k(w), k’ = k(w’) are the solutions of w? = /* tanh d’k’. As an 
g 
example, he showed s(w) of sw) = s'(w) + s@), for the following type spectrum, 
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