oncoming wave, and partial energy destruction is accomplished even before that 

 wave reaches the breakwater. If the walls were not perforated, total reflec- 

 tion would occur on the face of the wall and the resultant high impact forces 

 would be transmitted to the mooring cables. Part of the forces would be 

 directed to oscillating the breakwater, thus inducing waves on the protected 

 side of the structure. In a perforated breakwater, that part of the incident 

 wave energy which is dissipated internally in the form of heat and eddies is 

 not available for such activity. 



a. Reflection Coefficients . Richey and Sollitt's (1969a, 1969b) linear- 

 ized differential equation describing the motion of the fluid in the break- 

 water chamber is 



(b 2 D) 3a 1 9 2 a 



a + — + — = A sin at (71) 



(2m 2 h 2 g) 3t a) 2 3t 2 



where 



A = depth-averaged dynamic pressure head amplitude 



a = water surface elevation in breakwater chamber 



b = breakwater chamber width 



D = linearized damping coefficient 



m = effective breakwater porosity 



h = breakwater depth 



g = acceleration due to gravity 



to = natural frequency of the breakwater system 



a = wave frequency 



Equation (71) has the form of a forced, damped oscillator which occurs fre- 

 quently in mechanical systems. Any system which behaves according to this 

 expression can be considered a resonator because a attains an absolute 

 maximum value at one particular wave frequency, a, referred to as the reso- 

 nant frequency. a decreases continuously for frequencies greater than or 

 less than the resonant frequency. Richey and Sollitt (1969a, 1969b) developed 

 an analytical expression for "the reflection coefficient, C , which must be 

 solved by iterative techniques. Nevertheless, the form of the expression 

 indicates that the system is frequency selective and behaves as a resonator; 

 i.e., the reflection coefficient, C , tends to unity as a approaches 

 either zero or infinity, and C attains a minimum value at some intermediate 

 value of a, the resonant frequency. Since the expression cannot be solved 

 explicitly for C , the reflection coefficient cannot be maximized to yield 

 the resonant frequency. However, iterative solutions show that resonance 

 occurs when the frequency of the incident wave approaches the natural fre- 

 quency of the breakwater system. By reasoning from the pertinent dimensions 

 and variables involved, it can be concluded that the reflection coefficient, 

 C , is functionally related to the breakwater geometry by 



