b = 



1.56 

 (1 + e-19-^"^) 



m = bottom slope 

 h, = water depth at breaking 



i = 43.75 (1 - e"^^"") 

 because it accounts for bottom slope and wave period. 



44. Once the incipient breaking point is defined, a mechanism is needed 

 to transform the breaking wave across the surf zone. The transformation 

 algorithm selected for use in RCPWAVE (Dally, Dean, and Dalr}miple 1984) uses 

 an energy flux basis. Through analogy with energy loss in a hydraulic jump in 

 a channel, the following equation is postulated for one-dimensional transfor- 

 mation of waves advancing in the -x direction: 



d(Ec ) 



g_ 



dx 



Ec^ - (Ec„) 



(39) 



where 



Ec = energy flux associated with the breaking wave 



K = rate of energy dissipation coefficient (set equal to 0.2 in 

 RCPWAVE) 



(Ec ) = stable level of energy flux that the transformation process 

 s seeks to attain 



The right side of Equation 39 is simply a dissipation term. The subscript s 



is used to denote the stable level of a variable. Substituting the linear 



2 

 wave theory estimate for E (E = 0.125 pgH ) into Equation 39 results in the 



following expression: 



d(H c ) 



g_ 



dx 



H^c 



- («Sl 



(40) 



45. Various field (Thornton and Guza 1982) and laboratory (Horikawa and 

 Kuo 1966) experiments have shown that, well into the surf zone, the wave 

 height tends toward a stable value which is proportional to the local water 

 depth. This relationship can be expressed as 



29 



