For the steepest slope tested, tangg = 1/1.5, the procedure 

 leads to consistent estimates o£ the reflection coefficient as 

 evidenced by the low value of the standard deviation. However, the 

 mean value of Rjn/'^p' "^^Z^^' ^^ somewhat different from unity. 

 Basically the measured reflection coefficients are on the average only 

 about 90 percent of the values predicted by the semiempirical procedure 

 developed here. The reason for this discrepancy may be sought in the 

 steep slope angle which violates the basic assumption made in the 

 theoretical analysis that the slope be relatively gentle. This 

 assumption, which is discussed in Appendix A, means that the horizontal 

 velocity is taken to be representative of the velocity parallel to the 

 bottom. For smaller slopes this is a fairly good assumption, but as 

 the slope becomes steeper the velocity parallel to the bottom may 

 approach U/cosBs where U is the horizontal velocity. This increase in 

 near bottom velocity will increase the energy dissipation due to bottom 

 friction and hence lead to smaller values of the reflection coefficient. 

 Since the details of the wave motion on a steep slope are not known, the 

 above discussion is only to be taken as a tentative explanation of the 

 discrepancy between observed and predicted reflection coefficients for 

 steep slopes. 



For steep slopes the reflection coefficient is generally close to 

 unity so this discrepancy may not be of a severe nature. It is 

 recommended that the procedure developed here be used also for steep 

 slopes with 1/2.0 < tanBg < 1/1.5 with a correction factor being applied 

 to the predicted reflection coefficient. For a slope of 1 on 1 . 5 this 

 correction factor is taken as <R^/Rp> (Table 23;for slopes between 1 on 

 1.5 and 1 on 2 an appropriate correction factor, smaller than unity, 

 may be chosen corresponding to a linear interpolation between the values 



of <R /R >. 



m p 



All experiments discussed so far were performed for a water depth, 

 hg = 1 foot (0-305 meter), in the constant depth part of the flume. A 

 separate short series of tests was performed with h^ = 16 inches 

 (0.41 meter) for a value of tang^ = 1/3.0 and a surface roughness 

 d = 2 inches (5 centimeters) . The results of these tests are shown in 

 Table 3. 



The comparison between predicted and measured reflection coefficients 

 presented in Table 3 shows an excellent agreement. It is of particular 

 interest to note that a reflection coefficient as low as 0.42 was 

 observed and predicted. Since the average rate of energy dissipation on 

 the slope is obtained from 



Ep = (1-R^) Ep , (130) 



in which Ep is the energy flux asscoiated with the incident waves, this 

 means that 80 percent of the incident wave energy is dissipated on the 



72 



