effects of slope geometry and incident wave characteristics leaving 

 the burden of expressing the influence of slope roughness on the wave 

 friction factor, f^^. This considerable reduction in experimental effort 

 is the reason for the theoretical development. Thus, the theoretical 

 analysis has identified the fundamental unknown parameter as the wave 

 friction factor, f^. For the method to be applicable an empirical 

 relationship for f^^ must be established and here the physical interpre- 

 tation of f as a wave friction factor may be used as a guide. 



For fully rough turbulent flow conditions, Jonsson (1966) found for 

 waves over a rough boundary that his wave friction factor is a function 

 of the boundary roughness, d, relative to the excursion amplitude, A^, 

 of the orbital particle motions above the bed, i.e., 



W W A, 



For fully developed steady flow over a rough boundary, the 

 characteristic length scale is the water depth and the friction factor 

 corresponding to fully rough turbulent flow conditions is a function 

 of the boundary roughness, d, relative to the depth of flow, 



f = f 4) • (112) 



w w ^h^ 



In the present context it is expected that the flow is a mixture 

 of a boundary layer-type flow (eq. Ill) and a fully developed flow 

 (eq. 112), and it may therefore be expected that the empirical formula 

 for the wave friction factor, f , in equation (110) is of the form: 



f = f (^ , ^) . (113) 



w w ^A, ' h-^ 

 b 



As a representative value of the excursion amplitude. A, , the 

 value obtained from the theoretical solution (eq. 91) evaluated at 

 X = is taken, i.e., 



s 



and h = h,-, is taken as a representative value of the depth. Thus, it 

 is anticipated that an empirical relationship 



d tang , 



f = f ( — n^T-^ , J-) , (115) 



w w ^ A ' h -^ ' ^ ^ 



' ' o 



for the wave friction factor exists. To determine this empirical rela- 

 tionship is the purpose of the experimental investigation described in 

 Section III. 3. 



59 



