1 ^N -2 ^e 



e - . ^ e 1/2 h "' 'AV 



^2C^ ^J> 



This equation shows that the width o£ the equivalent breakwater may 

 be determined from knowledge of the configuration of the trapezoidal, 

 multilayered breakwater and the corresponding head differences, AH and 

 AHj,. 



As described in Section IV. 1 the equivalent breakwater is subject 

 to an equivalent incident wave of amplitude aj given by equation (146). 

 A simplified analysis of the interaction of incident waves and a 

 rectangular homogeneous breakwater of small width relative to the length 

 of the incident waves was presented in Section II. 2. a. This simplified 

 analysis essentially neglected unsteady effects and any phase difference 

 between the incident, reflected, and transmitted waves. The runup on 

 the seaward slope is for this analysis given by equation (38) and this 

 runup is taken as a representative value of the head difference, AH , 

 across the equivalent breakwater. With this assumption, which neglects 

 the influence of a transmitted wave of small amplitude, one obtains 



AH = (1 + RJ a^ = (1 + RJ R^^ a. , (159) 



e ^ I^ I ^ I II 1 ^ -^ 



in which R. is the reflection coefficient of the equivalent breakwater. 



The value of the head difference across the trapezoidal breakwater, 

 AH-p, is in accordance with the argument presented for the equivalent 

 rectangular breakwater taken as the runup on the seaward slope of the 

 trapezoidal breakwater. This runup may in principle be determined by 

 the procedure developed in Section III of this report. However, there 

 is reason to believe that such an estimate, which would correspond to 

 an impermeable slope, would be somewhat on the high side. In general 

 one may, however, take 



AH^ = 2R^ a. , (160) 



where R^ is the best estimate available for the ratio of the runup to 

 the incident wave height H. = 2a. for given slope characteristics. If 

 R^ is taken as determined from Figure 16 the estimate of AH-p is expected 

 to be conservative. 



Equations (159) and (160) show that the ratio 



AH^ (1 . Rj)Rjj 



\Hj, 



2R 

 u 



(161) 



86 



