2. Analytical Investigation . 



A dimensional analysis of the pertinent variables involved indicates that 

 the transmission coefficient, C t = n t /R ± , is functionally related to at least 

 five other dimensionless parameters, all of which are totally independent from 

 each other. 



C t = f - , - , ^ , ^ , -M (46) 



c \L d L I w / 



where 



C f = wave transmission coefficient 



H t = height of transmitted wave 



H. = height of incident wave 



Z = effective width of structure 



&u = ballasted length of sloping float 



L = incident wavelength 



d = water depth 



w = weight of unit length of sloping float 



w^ = weight of internal ballast in a unit length of sloping float 



The coefficient of transmission, C t , depends on the wavelength and the water 

 depth relative to the length of the float, the wave steepness, and two param- 

 eters which govern the distribution of mass of the ballasted float (effec- 

 tively, the moment of inertia and the location of the center of gravity). 

 Both mathematical modeling and physical experimentation were undertaken to 

 determine the functional relationship between these independent variables. 



Raichlen and Lee (1978) studied initially the dynamics of a sloping-float 

 breakwater to determine the forces in the mooring lines and the motion of the 

 semisubmerged pontoons under wave action. Mooring forces can be predicted by 

 evaluating the pressure distribution around the breakwater as a function of 

 time, the forcing function which causes the breakwater motion. The geometry 

 of an individual barge element initially considered is shown in Figure 55. 

 For the theoretical investigation, waves are considered to be approaching 

 normal to the barge and the mathematical model is two-dimensional. The 

 possible motions of the barge when referenced to this orientation are surge, 

 heave, and pitch. Raichlen and Lee's (1978) objective was to predict the 

 tension in the mooring line as a function of time due to incident waves and 

 determine the motion of the barge center of gravity. The approach to the 

 problem is to develop the equations of barge motion, written in terms of the 

 unknown pressure distribution on the body defined in terms of the time 

 derivative of the velocity potential, a function of the incident wave height, 

 period, water depth, and inclination angle of the barge. The problem is 

 complicated by the interrelationships of motions and waves, and is similar to 

 the problem of defining the motions of a moored ship. 



96 



