II. THEORETICAL ANALYSIS 



In the analysis of complex systems such as floating breakwaters, 

 there is a great need for model-scale experiments to predict their per- 

 formance and provide data for the application of rational engineering 

 design principles. Full-scale measurements are also extremely valuable 

 in verifying scaling relationships and in providing confidence that the 

 data obtained from smaller scale experiments are reasonable. 



When one considers the myriad possible breakwater configurations 

 which have been proposed to date and the different conditions which pre- 

 vail at each potential breakwater site, the number of required model 

 tests and the attendant expense are very large. To avoid this expense 

 and also to permit parametric studies aimed at obtaining optimum break- 

 water configurations, a theoretical model was developed. The goal was 

 to theoretically predict the performance which could be measured in la- 

 boratory studies or at prototype installations. 



The initial restriction imposed on the theoretical model was to 

 consider only two-dimensional conditions. Under this restriction the 

 breakwater is assumed to be very long in one direction with long-crested 

 waves approaching so that their crests are parallel to the long axis of 

 the breakwater. At most breakwaters where the wave climate results from 

 wind- generated waves, this condition would rarely be approached. How- 

 ever, experiments performed using a boat wake to generate incident waves 

 on the beam and at an angle to a breakwater indicate larger breakwater 

 motions and larger transmitted waves when the incident wave crests 

 approach parallel to the long axis of the breakwater (Stramandi, 1975). 

 As a design tool, a two-dimensional theory provides information on the 

 worst conditions which might be expected to occur. In addition, the 

 extensive two-dimensional wave-channel experiments provide the data need- 

 ed to test the theoretical model. 



Throughout the development of the theoretical model, every attempt 

 was made to orient the model toward providing a useful tool applicable 

 to realistic problems. To perform the calculations the user need only 

 know the incident wave frequencies of interest, the contour of the 

 breakwater cross section (catamaran- or trimaran-type cross sections are 

 permitted) , and the physical properties of the breakwater (these include 

 mass, mass moment of inertia, and the static restoring-force coeffi- 

 cients) . 



The approach used here has been to employ the techniques which naval 

 architects have developed to deal with ship motion problems. Mathema- 

 tically, the hydrodynaraic equations are formulated in terms of a- boun- 

 dary value problem for the velocity potential. Solution of this complete 

 problem is presently impossible because the free-surface boundary condi- 

 tion is nonlinear. An approximate solution may be obtained if restric- 

 tions are imposed on the boundary value problem, and the procedure of 

 linearization is applied. The restrictions limit the applicability of 



