the width of the breakwater, I, relative to the incident wavelength, L, 

 a set of simple formulas was derived for T and R, equations (35) and 

 (36]. 



From equations (35) and (36) as well as from Figures 2 and 3 it is 

 seen that the transmission coefficient increases and the reflection 

 coefficient decreases with decreasing values of nkoJ?-. This is in agree- 

 ment with expectations since low values of k^Ji indicate a long wave 

 relative to the width of the structure thus essentially making the 

 structure transparent to the incident waves. An increase in frictional 

 effects, which are accounted for by the linearized friction factor, f, 

 is seen to cause an increase in the reflection coefficient and a 

 decrease in the transmission coefficient. In this respect it is seen 

 from equation (57), which is the explicit solution for the linearized 

 friction factor, f, that the frictional effects increase with increasing 

 amplitude of the incident waves, thus reflecting the nonlinear nature 

 of the flow resistance of the porous structure. 



The procedure developed is, through the adoption of empirical 

 relationships for the hydraulic properties of the porous medium, 

 entirely explicit. The required information is the incident wave 

 characteristics (a^^ and L) , the breakwater geometry (£ and \\q) , and the 

 characteristics of the porous material Cstone size, d, and porosity, n) . 

 The ability of the procedure to predict experimentally observed trans- 

 mission and reflection characteristics of crib-style breakwaters was 

 demonstrated. It was found that the procedure yields excellent predic- 

 tions of the transmission coefficient whereas some discrepancy between 

 observed and predicted reflection coefficients was noted. This 

 discrepancy may be partly attributed to experimental error in the 

 determination of the reflection coefficient. 



Numerical Example . The following numerical example is included 

 to illustrate the application of the procedure developed for the 

 prediction of transmission and reflection coefficients of a porous 

 rectangular breakwater. The information which is assumed available is 

 listed in Table 1. To illustrate the assessment of scale effects the 

 problem is considered both for a prototype and for a Froude model with 

 length scale 1 to 25. 



As discussed in Section I the procedure developed in this Section 

 of the report accounts for the partition of incident wave energy among 

 reflected, transmitted, and internally dissipated energy. Thus, the 

 present Section forms part of the ultimate procedure for the prediction 

 of reflection and transmission characteristics of trapezoidal, multi- 

 layered breakwaters. The energy dissipation taking place on the seaward 

 slope of a trapezoidal breakwater is discussed in Section III which 

 also includes a numerical example. The incident wave characteristics 

 listed in Table 1 correspond to the incident wave assumed in the 

 numerical example presented in Section III, Table 4, after subtracting 

 the amount of energy dissipated on the seaward slope of a trapezoidal 



41 



