the reflection coefficients for the breakwater and smooth impermeable slope 

 is approximately the same because breakwater overtopping is small. 



The wave reflection coefficient decreases as the wave height or steepness 

 increases for a subaerial breakwater, but shows the opposite trend for a sub- 

 merged breakwater (Fig. 10). There is a slight increase in the reflection 

 coefficient as the wave height increases for the conditions tested. 



The variation of the wave transmission coefficient for a smooth impermeable 

 breakwater is the reverse of that found for the reflection coefficient. If the 

 wave runup is less than the breakwater freeboard there is no wave transmission. 

 As soon as the runup exceeds the crest of the breakwater, wave transmission by 

 overtopping occurs. All other factors being fixed, as the wave height increases 

 the size of the runup and the transmission by overtopping coefficient increase 

 (Fig. 10); as the ratio of the water depth to structure height, dg/h, ap- 

 proaches 1.0 the transmission coefficient increases. Even with zero freeboard 

 (d /h = 1) there is some increase in the wave transmission coefficient as wave 

 steepness increases (Fig. 10). However, for a submerged breakwater of fixed 

 geometry the wave transmission coefficient declines as wave height or steepness 

 increases (Fig. 10) . 



b. Estimating Wave Transmission by Overtopping Coefficients . Wave trans- 

 mission by overtopping is closely related to wave runup and overtopping of a 

 breakwater. Weggel (1976) found that overtopping rates are a function of the 

 ratio of the structure freeboard, F, to the runup, R, on a similar structure 

 high enough to prevent overtopping (Fig. 7). Cross and Sollitt (1971) also 

 recommend the dimensionless parameter, F/R, for predicting wave transmission 

 by overtopping coefficients. 



Several methods are available for estimating wave runup on smooth imperme- 

 able slopes; some of these methods are summarized in Stoa (1978). The runup 

 prediction equation developed by Franzius (1965) gives the best estimate of 

 wave runup for predicting wave transmission coefficients. The runup is given by 



R = HC^ (0.123 ^j (10) 



where L is the local wavelength determined from linear theory using 



(^) 



tanh {^^^] (11) 



2-n 



and Cj, C2, and C3 are empirical coefficients. Franzius suggests values 

 for the coefficients, but improved coefficients were obtained in this study 

 using the data of Saville (1955) and Savage (1959) with a nonlinear error 

 minimization computer routine. The recommended values of the empirical coeffi- 

 cients are given in Table 2. These values are linearly interpolated to estimate 

 values of the coefficients for other slopes. An advantage of using equation 

 (10) is that it includes effects of wave height, structure slope, wave steepness, 

 and the ratio of water depth to wave height on wave runup. 



The runup on rough slopes is also a complex function of many factors (Stoa, 

 1978). Madsen and White (1976) give an analytical-empirical model for estimating 



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