a transfer function can be deduced, analogous to the wave height line spec- 

 trum, to develop a line force spectrum 



2 [2 FUp (2tt Af i )] 



1/2 



(51) 



From equation (51), a continuous force spectrum, F(o).), can be established 

 for determining the maximum probable force. 



The size of barges under consideration for use as a sloping-float break- 

 water by either the Navy or the COE is expected to yield beneficial effective- 

 ness for wave periods up to 7 seconds. The Pierson-Moskowitz open-ocean wave 

 spectrum with peak at 7 seconds is shown in Figure 66 as the incident wave 

 climate. Equation (49) can be utilized to yield the wind velocity required to 

 generate this spectrum. The transformation shown in equation (50) is used to 

 obtain the incident wave height spectrum, presented in Figure 67(a). These 

 heights represent periodic waves of the indicated frequency which, when 

 superposed on each other, yield the irregular wave field approximating the 

 continuous spectrum of Figure 66. For each wave height in Figure 67(a), a 

 transmission coefficient, C t (u)-), can be obtained from the experimental data 

 corresponding to the appropriate configuration. The product of these coeffi- 

 cients and the incident wave height, (C t (u^) x H^), produces the transmitted 

 wave height spectrum, also shown in Figure 67(a). The continuous frequency 

 spectrum of the transmitted wave height can be obtained by applying equation 

 (48); this spectrum is shown in Figure 66. The mooring forces pertaining to 

 the individual wave periods are obtained in an analogous manner, and are shown 

 in Figure 67(b), with the continuous force spectrum shown in Figure 67(c). 



- 







Incident vv 







1 7 ' 





H l/3 



6.44 It 









U 



31 5lt/5 

 7 s 



- 







"l/3 



1 19 It 



- 





\ Inc.dem 



y 







- 



/ Transmuted 

 / 1 — L 



i i 



1 



1 



04 UOB 



12 1G 









Frequency, Hz 



Figure 66. Two-dimensional experimental investigation of incident 

 and transmitted Pierson-Moskowitz wave spectrum for 7- 

 second peak, sloping-float breakwater with bottom clear- 

 ance at a 25-foot water depth (after Raichlen, 1978). 



112 



