raw data (R '^ 0.62) and from the corrected data (R = 0.88). By using 

 this procedure it was found that reflection coefficients determined 

 from the variation of the amplitude of the first harmonic motion 

 generally were within a range of +_ 0.02 whereas a variation as large 

 as 0.45 < R< 0.75 was found for a single experimental run when the raw 

 data were used directly. With the intended use of the data in mind, it 

 is quite obvious that the accurate, although tedious, procedure of 

 subjecting the wave records to a Fourier analysis had to be used 

 throughout this study. 



The pronounced effect of second or higher harmonic motions on the 

 accurate determination of the reflection coefficients from experimental 

 data is closely related to high values of the reflection coefficient 

 since this entails the near vanishing of the first harmonic motion near 

 the nodes. However, it should be noted that the decision of whether or 

 not to use the time-consuming Fourier series procedure cannot be based 

 solely on the magnitude of the reflection coefficient. Test number 33 

 (App. B) showed pronounced higher harmonic effects with a reflection 

 coefficient of R = 0.60 whereas test number 62 exhibited only insignifi- 

 cant higher harmonics although the reflection coefficient for this test 

 was 0.80. A visual inspection of the recorded wave profile at each 

 station generally led to an accurate assessment of whether or not the 

 Fourier series analysis was called for. 



c . Empirical Relationship for the Wave Friction Factor, f . To 

 establish a sufficient data base from which an empirical relationship 

 for the wave friction factor, f^, may be obtained, two series of 

 experiments were performed for values of the slope (tanBg) = 1/2.0 and 

 1/3.0, respectively. For each slope a total of 48 experiments were 

 performed as discussed in Section III. 3. a. The data were analyzed in 

 the manner described in Section II1.3.b to yield values of the reflection 

 coefficient, R. With the value of R determined for each experimental 

 run and the value of Hs/L known. Figure 15 wds used to obtain (}> and the 

 corresponding value of f was obtained from equation (116). 



Anticipating an empirical relationship for f^^ of the type suggested 

 by equation (115) the semiempirical values of f^ are plotted against the 

 the value of |A|/(d tangg) in Figure 22. Although exhibiting a consid- 

 erable amount of scatter the data do form four reasonably well-defined 

 bands depending on the relative roughness, d/hg, in conformance with 

 the anticipated behavior. The experimental data and the details of the 

 analysis leading to Figure 22 are presented in Appendix B. 



Two families of straight-line approximations of the data are shown 

 in Figure 22. One, the dashlines, has a 1 on 1 slope and leads to an 

 extremely convenient empirical relationship for the wave friction factor 



, -0.74 d tan3 

 fw= 0-25 (^ -fAT^ • ^^24) 



67 



