the solution to cases of small incident wave amplitude and small motion 

 response of the breakwater. 



When using the linearized theory which is presented here, one must 

 be well aware of the limits of applicability which are imposed on the 

 results in order to permit the formulation of a tractable mathematical 

 problem. Care must also be exercised because these restrictions may 

 exclude phenomena which occur in nature from appearing in the mathemati- 

 cal analysis. For instance, field observations clearly demonstrate 

 the occurrence of mooring line force oscillations at periods greater than 

 those which could be attributed directly to wind-generated wave exci- 

 tation. Using a linearized approach, these long-period oscillations 

 would not appear in the analysis . A theoretical model which includes 

 nonlinear behavior of the system is required if these long-period os- 

 cillations are to be included. 



A possible nonlinear mechanism for the transfer of wave energy to 

 lower frequencies has been postulated and is presented to supplement the 

 linear analysis. 



Linear Theoretical Model , 



The problems involved in theoretically predicting the performance of 

 a two-dimensional floating breakwater are illustrated in Figure 2. Here 

 an incident wave approaches the breakwater on the beam. A part of the 

 energy contained in the incident wave is reflected, part passes beneath 

 the breakwater, and some is lost through dissipation. Another part of 

 the incident wave energy excites the motions of the breakwater. These 

 motions are restrained by the mooring system. The oscillating break- 

 water in turn generates waves which travel away from the breakwater in 

 the directions of the reflected and transmitted waves. The total trans- 

 mitted wave is the sum of the component which passes beneath the break- 

 water and the components generated by the breakwater motions . The total 

 reflected wave is composed similarly. 



In completing the calculations, the information which is of most 

 interest to the designer includes: 



(a) Total transmitted and reflected waves including their 

 components . 



(b) Wave forces on the breakwater. 



(c) Motions of the breakwater. 



(d) Forces on the mooring lines. 



For the two-dimensional breakwater, definitions for the motions are 

 shown in Figure 2. Sway is defined as the oscillation perpendicular to 

 the long axis, or along the x-coordlnate axis. Heave is the vertical 



