(2) Mooring Forces . The variation of the mooring force with the 

 relative depth, kd, is presented in Figure 65 for waves of constant height 

 and the condition of a bottom-supported barge. A comparison of Figure 65 and 

 Figure 58 (no bottom clearance) indicates significant differences in the shape 

 of the curves; for the case with a gap, the maximum mooring force is shifted 

 to smaller wave periods. For wave heights up to 8 feet, the mooring force 

 increases compared to the case of no bottom clearance. For a 10-foot wave 

 height, the maximum mooring force decreases from about 160,000 pounds at no 

 gap to about 130,000 pounds with the gap. For the shorter waves and the 

 larger wave heights, there is no significant difference between the mooring 

 forces for the case with or without a gap. This is probably due to the fact 

 that the velocities near the bottom are smaller for the shorter waves than 

 they are for the longer waves, represented by values of kd less than approx- 

 imately 0.6. 



4. Application to Random Open-Ocean Waves . 



Raichlen's (1978) experimental study dealt with the forces in the mooring 

 system and the transmission characteristics of the partially flooded barge 

 exposed to periodic waves. The results for an irregular wave climate on the 

 ocean surface can be interpreted, using a wave spectra model. A commonly used 

 spectrum in oceanographic work is the Pierson-Moskowitz spectrum 



2 

 ag 



S(w) = — — (48) 



w 5 exp[-e(g/Ua))' t ] 



where 



g = gravitational acceleration 



to = wave circular frequency 



U = wind velocity at standard height of 19.5 meters above sea level 



3 = 0.74, commonly used value 



a = 0.0081, commonly used value 



The peak frequency of the spectrum described by equation (48) is 



(r) (u) (49) 



P \5 / \ U 



from which the windspeed can be obtained corresponding to that peak frequency. 

 It can be easily shown that the wave spectrum, S(w), can be converted to a 

 line spectrum of wave height as 



H. = 2 [2 SU.) (2tt Af.)] 1/2 (50) 



where Afj_ is the frequency bandwidth corresponding to the spectral estimate 

 S(to i ) centered at u^. If a mooring force, F i , is defined which corre- 

 sponds to the wave height, H^, from mooring force curves such as Figure 65, 



110 



