An extensive experimental investigation is performed to establish 

 an empirical relationship for the wave friction factor. The experimental 

 investigation utilizes measured reflection coefficients of rough 

 impermeable slopes in conjunction with the theoretical results to obtain 

 values of the wave friction factor. The experimental investigation 

 shows the need for a method for obtaining accurate estimates of reflection 

 coefficients from experimental data. Such a method is developed and the 

 end product of the experimental investigation is empirical relationships 

 for the wave friction factor. The experiments are performed with slope 

 roughnesses modeled by gravel and are therefore applicable only when the 

 slope roughness elements consist of natural stones. Separate experimental 

 investigations should be carried out to establish empirical relationships 

 for f^^, corresponding to other surface roughness elements, e.g., concrete 

 armor units. 



The result of the combined use of the empirical relationship for f 

 and the theoretical developments is a "semiempirical" procedure for 

 estimating the reflection coefficient and hence the energy dissipation 

 of rough slopes. The procedure requires knowledge of the incident wave 

 characteristics (amplitude and wavelength) and the slope characteristics 

 (slope angle and stone size). The procedure was tested against a 

 separate set of experiments and yielded quite accurate results. 



2. Theoretical Solution for the Reflection Coefficient of Rough 

 Impermeable Slopes . 



The problem to be considered is illustrated in Figure 14. 



Figure 14. Definition sketch. 



With the assumption of relatively long incident waves the governing 

 equations for arbitrary bottom topography are derived in Appendix A, 

 equations (A-20) and (A-21). The linearized forms of these equations 

 are given by equations (A-24) and (A-25) 



48 



