and 



|a I 



T = — ^ = T R,, . (150) 



a. Ill 



The approximate procedure described above is used to predict the 

 reflection and transmission coefficients corresponding to the laboratory 

 experiments performed by Sollitt and Cross (.1972). When considering 

 that the predicted results are obtained without any attempt being made 

 to fit the experimentally obtained reflection and transmission 

 coefficients from Sollitt and Cross, the comparison between predictions 

 and experiments is favorable. 



2. Determination of the Equivalent Rectangular Breakwater . 



From the description given of the approximate method for obtaining 

 the reflection and transmission coefficients of a trapezoidal, 

 multilayered breakwater, the missing link for carrying out this analysis 

 is the determination of the hydraulically equivalent homogeneous 

 rectangular breakwater. 



In Section II. 2. a it was shown that a simple analysis, which 

 essentially neglected unsteady effects, gave transmission and reflection 

 coefficients (eqs. 45 and 46) equal to those obtained from the more 

 complete analysis for structures of small width relative to the incident 

 wavelength (eqs. 35 and 36). This observation suggests that a rational 

 and reasonably simple determination of the hydraulically equivalent 

 breakwater may be based on steady flow considerations. Therefore, a 

 hydraulically equivalent breakwater is taken as the homogeneous 

 rectangular breakwater which gives the same discharge, Q, as the 

 discharge through the trapezoidal, multilayered breakwater. This 

 definition will, according to the simple analysis presented in 

 Section II. 2. a, preserve the equality of transmission coefficients for 

 the two structures and hence essentially give the same internal 

 dissipation. This definition of the equivalent breakwater is illustrated 

 schematically in Figure 23. 



Figure 23 shows schematically a trapezoidal, multilayered breakwater 

 consisting of several different porous materials. These porous materials 

 are identified by their stone size, d , and their hydraulic character- 

 istics, 3 , in the flow resistance formula (eq. 6). To keep the 

 following determination of the equivalent breakwater reasonably simple, 

 the flow resistance is assumed to be purely turbulent although in 

 principle it is possible to perform the determination of the equivalent 

 breakwater based on the more general form of the Dupuit-Forchheimer 

 resistance formula. Since the energy dissipation associated with the 

 top layer of stones on the seaward slope has been accounted for, the 

 rectangular homogeneous breakwater which accounts approximately for the 

 internal dissipation should be hydraulically equivalent to the trapezoidal, 

 multilayered breakwater with the top layer of cover stones removed. 



82 



