where 



R = the vertical height of runup above the Stillwater level 



u = the current velocity of the surge at the shoreline 



f = the friction factor 



S = the ground slope 



g = gravitational acceleration 



A = a coefficient 



Adapting the work of Keulegan (1950), they obtain a maximum value of 

 A = 0.5. Using a value for u given by 



u 



= 7(g h J 1/2 (311) 



s as 



where h s is the surge height at the shoreline, taking the friction 

 factor, f, as 



8g 

 f = — (312) 



where C/j is the Chezy coefficient, and using the maximum value for A, 

 equation (310) reduces to 



R 6 



h" = " 3-2g (313) 



1 + 



C, 2 S 

 n 



As C^ varies with depth, this equation would predict that the relative 

 runup R/h s varies between a prototype and model unless proper roughness 

 scaling is used. Because C-u decreases with increasing roughness, the 

 relative runup would decrease as the roughness increases. Also, as slope 

 increases, the relative runup increases. As the slope approaches infinity 

 (a vertical wall), the relative runup R/h = 6. This value is somewhat 

 higher than experimentally obtained values. Camfield and Street (1967, 

 1968) obtained values of relative runup between 4.5 and 5.0 from solitary 

 wave experiments for breaking waves running up on a vertical wall. Equa- 

 tion (313) does not consider the effects of wave period. 



Freeman and Le Mehaute (1964) noted that coefficient A in equation 

 (310) should be somewhat less than 0.5. Kishi and Saeki (1966) indicate 

 that the value of A decreases as the slope decreases, which is consist- 

 ent with Freeman and Le Mehaute that the value of A depends on the form 

 of the wave at the shoreline. 



154 



