H = rh 



s 



(41) 



where 



H = stable wave height 



r = proportionality coefficient (set equal to 0.4 in RCPWAVE) 

 Equation 40 can now be rewritten as 



dx 



H^c 



- {^'^\) 



= D 



(42) 



46. This surf zone wave transformation model, extended to two dimen- 

 sions, can be incorporated into the conservation of wave energy equation 

 (Equation 28) by simply adding a dissipation term D to the right side. The 

 function D must now represent dissipation in the direction of wave prop- 

 agation. Also for dimensional consistency, the term D must be multiplied by 

 the wave celerity and the magnitude of the wave phase gradient, and the wave 

 height must be replaced by the wave amplitude function. In vector notation, 

 the energy equation becomes 



V 0) (a cc Vs) = r- 



H' 



a cc |Vs| - 



,2a) 



r^h^cc IVsl 

 g ' 



(43) 



This equation can be thought of as being valid both inside and outside the 

 surf zone. Outside, the coefficient k is zero, and the equation reduces to 

 Equation 28. 



47. All discussion relating to wave transformation within the surf zone 

 up to this point has addressed the problem of determining wave heights. The 

 problem of wave phase must be addressed also. Diffraction effects are assumed 

 to be negligible inside the surf zone. Therefore, the wave number k is as- 

 sumed to accurately represent the magnitude of the wave phase function gradi- 

 ent. The linear wave theory assumption that the waves are irrotational also 

 will be assumed to remain valid inside the surf zone. Consequently, wave 

 angles are computed in the same manner as outside the surf zone. Details con- 

 cerning the numerical solution inside the surf zone can be found in Ebersole, 

 Cialone, and Prater (1986). 



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