the x-direction). The last term is obtained from the time derivative of the 

 velocity potential and, hence, the equation of motion is fully defined in 

 terms of the incident wave amplitude. To verify the equations of motion of 

 the sloping float breakwater, and to provide the Naval Civil Engineering 

 Laboratory with useful information for a full-scale prototype test program of 

 this structure, Raichlen (1978) tested a statically and dynamically accurate 

 scale model of the sloping-float and mooring system so that both the mooring 

 forces and the transmission characteristics of such an inclined pontoon could 

 be estimated with confidence. 



3. Experimental Investigation. 



Particular objectives of Raichlen' s (1978) experimental program were to 

 investigate the effect on the mooring forces and transmission characteristics 

 of the location of the mooring point on the barge, of a gap under the end of 

 the barge which rests on the sea floor, and of structures placed atop the 

 inclined pontoons to minimize wave overtopping. All experiments were con- 

 ducted using periodic incident waves with a 25-foot prototype depth. Since 

 actual incoming wave energy has a spectral distribution, the regular wave 

 experiments were also analyzed with respect to irregular wave application. 

 The wave tank used in the study was about 120 feet long, 3 feet wide, and 3 

 feet deep. All data were obtained without reflection influences. 



a. Structure Resting on Bottom (No Bottom Clearance) . The first series 

 of experiments conducted by Raichlen (1978) dealt with a mooring configuration 

 where the mooring point on the barge was located 29.5 feet from the seaward 

 end of the barge. The center of gravity of the flooded barge at a depth of 

 72.5 feet was located 52.65 feet from the seaward end; thus, the mooring point 

 was located 23.15 feet above the center of gravity of the flooded barge. The 

 bottom of the barge was positioned on the bottom of the flume. Experiments 

 were conducted for 3 different prototype wave heights (3, 6, and 10 feet); for 

 each wave height, the barge was exposed to about 15 different wave periods at 

 a 25-foot depth. The periods varied from 5.2 to 18.7 seconds, the full range 

 of the important wave periods expected in an irregular sea at the site of 

 potential field experiments. For each wave period, curves of prototype 

 mooring force versus wave height and transmission coefficient versus wave 

 height were determined. The experimental configuration is shown in Figure 56; 

 experimental results are presented in Figures 57 and 58. 



(1) Effect of Wave Height on Transmission Coefficient. For dimen- 

 sionless depths, kd (where k = 2it/L) greater than approximately 0.6, there 

 is a significant increase in the transmission coefficient with increasing wave 

 height. Part of this nonlinear effect is due to waves overtopping the seaward 

 edge of the structure. For example, for a 7-second wave period, the transmis- 

 sion coefficient varies from approximately 0.15 for a 2-foot-high wave to 

 nearly 0.55 for a 10-foot-high wave (Fig. 57). There is transmission both 

 over and under the structure as the barge is able to move off the bottom 

 during testing. In addition, one of the major factors influencing transmis- 

 sion is the motion of the barge itself, which acts as a wave generator. For 

 large incident waves, the generation process is probably not linear. 



(2) Effect of Wave Height on Mooring Forces . The variation of the 

 mooring line force with kd is shown in Figure 58 for constant wave heights 

 varying from 2 to 10 feet. The angle of inclination of the barge with the 



98 



