The equation can be solved using either finite element (for example, Berkhoff 

 1972, Houston 1981) or finite difference methods (for example, William, 

 Darbyshire, and Holmes 1980). Since transmission and reflection boundary con- 

 ditions are easily implemented into these solution schemes, this approach is a 

 popular one for modeling tsunami propagation and for solving problems involv- 

 ing the response of harbors to short and long waves. This method becomes 

 computationally infeasible for large scale, open coast, short-wave problems 

 because of its great expense. 



27. The model RCPWAVE is an alternative approach for solving the open 

 coast wave propagation problem. It addresses the processes of refraction and 

 diffraction and can be applied to a large region quite economically. The 

 model also contains an algorithm which estimates wave conditions inside the 

 surf zone. This wave breaking model is an extension of the work of Dally, 

 Dean, and Dalrymple (1984) to two horizontal dimensions. 



Wave transformation outside 



the surf zone; theoretical basis 



28. The velocity potential function for linear, monochromatic, plane 

 waves can be represented by the following expression: 



(|) = a e^^ (26) 



where 



a(x,y) = wave amplitude function equal to - — -z — '-^— 



H(x,y) = wave height 



s(x,y) = wave phase function 

 Here the velocity potential function describes only the forward scattered wave 

 field. No considerations are given to wave reflections. By substituting this 

 expression for the velocity potential into Equation 24 and solving the real 

 and imaginary parts separately, two equations can be derived (Berkhoff 

 (1976)), namely. 



1 



3x ay g ^ ^ ' 



+ k^ - IVsl^ = (27) 



V • (a^cc Vs) = (28) 



g 



22 



