The other, the full lines, has a 1 on 0.7 slope, (Fig. 22) and 

 corresponds to an empirical relationship for the wave friction factor, 



-0.5 d tang 0.7 

 f^=0.29(^) i-^xr-) ■ (125) 



o ' ' 



The second relationship, equation (125), is superior to equation 

 (124) in representing the data from single subsets of the experiments 

 in which only the amplitude of the incident waves varied. One such 

 typical subset of data points, corresponding to d = 2 inches 

 (5 centimeters), T = 1.8 seconds and tan $g = 1/2.0, is indicated by 

 full circles with arrows in Figure 22. The slope of a line connecting 

 these data points is approximately 1 on 0.7; this slope reflects the 

 experimental observation that the reflection coefficient generally 

 decreased with increasing height of the incident waves. This is a 

 consequence of the nonlinear nature of the energy dissipation on the 

 rough slope and equation (125) is therefore to be considered superior 

 to equation (124) which is included primarily because it possesses some 

 convenient features. 



4. Comparison of Predicted and Observed Reflection Coefficients 

 of Rough Impermeable Slopes . 



With the empirical relationships for f^, (eqs. 124 or 125), the 

 semiempirical procedure discussed in Section III.2.b for the prediction 

 of the reflection coefficient of rough impermeable slopes is now 

 complete. UTiereas the theoretical analysis identified the wave friction 

 factor as the physically fundamental parameter, the friction angle, <i>, 

 is the important parameter for the use of Figure 15. However, by merely 

 introducing the empirical relationship for f^^ in equation (109) an 

 implicit equation for (J) may be obtained. 



By introducing equation (124) in equation (109) the following 

 equation for <() is obtained: 



, 0.26 

 tan2(t) = 0.25(^) F . (126) 



This equation is in principle implicit, since the slope friction constant 

 Fg, as seen from Figure 17 is a function of <)). However, for small values 

 of Jig/L (£5 /L < 0.3), Fg is only a weak function of ^ and equation (126) 

 may therefore be regarded as an explicit equation for (ji requiring 

 knowledge of only the relative slope roughness, d/h^. This may be a 

 somewhat surprising result since it means that the value of the slope 

 friction angle, 4), and hence the reflection coefficient obtained from 

 Figure 15 is independent of the amplitude of the incident waves. As 

 mentioned previously the main part of the experiments presented in 



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