It is also necessary to account for the dependence of C^ on the 



varying height, h, of the surge traveling up the onshore slope. Noting 



that, for uniform flow, C^ can be related to the Manning roughness 

 coefficient n by 



2 h 1/3 



in metric units (the right side of eq. 314 is multiplied by 2.22 for 



the foot-pound-second system of units) , and that a plot of h 1/3 versus 



h for <_ h <_ h s will give an average value of h = 0.75 h„. It is pro- 

 posed equation (314) can then be written 



0.91 h 1/3 

 cj: = ^— (315) 



in metric units. This allows equation (310) to be rewritten as 



(316) 



R 



1 (1 + A)(l + 2A) 



h 



s 



2A 2 ( 8gn 2 



0.91 A 2 S h 1/3 

 s 



in metric units (the coefficient 0.91 on the right side is equal to 2.02 

 in the foot-pound-second system of units). Kishi and Saeki give a log- 

 log plot for A versus S, with A = 0.25 when S = 0.03, and A = 0.04 

 when S = 0.07. Values of A were only obtained for that range of slopes. 

 Also, the effect of wave period on the results was apparently not inves- 

 tigated. 



Camfield and Street's (1967) laboratory results for borelike solitary 

 waves running up a 4° slope (S = 0.0699), fronted by a slope S = 0.01, 

 give a total relative runup R/H g of 3.3 for a value of h g = 0.061 meter 

 (0.2 foot) on a smooth aluminum slope. Using a value of n = 0.01 in 

 equation (316), and using a value of A = 0.4 suggested by Kishi and 

 Saeki (1966), R/h g would have a calculated value of 2.67, which is 

 close to the measured value. Kishi and Saeki obtain similar results for 

 rough slopes. As previously mentioned, the runup values of Camfield and 

 Street (1967) include a shallow flooding which may not be an accurate 

 prediction of prototype conditions. If only the greater water depths 

 were considered, such as shown in Figure 53, then the measured value of 

 R/h s =1.0. 



It should be noted that the above equations assume a uniform slope. 

 For runup on a shoreline where the slope varies, it would be necessary 

 to use a numerical solution to determine the limits of the runup. Freeman 

 and Le Mehaute have carried out numerical calculations for slopes S >_ 0.1, 

 but present no results for very flat slopes. Very little data exist to 

 verify such equations or to determine their full range of application. 



155 



