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 5. 



39. Discussion relating to wave transformation within the surf zone 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 assumed to accurately 

 represent the magnitude of the wave phase function gradient. The linear wave 

 theory assumption that the waves are irrotational also will be assumed to re- 

 main valid inside the surf zone. Consequently, wave angles inside the surf 

 zone are computed in the same manner that was used outside the surf zone. 

 Numerical solution 



40. The numerical procedure for computing wave angles inside and out- 

 side the surf zone is the same. This section documents only the solution 

 scheme used to determine breaking wave heights. The finite difference form of 

 the wave energy equation outside the surf zone (Equation 26) can be expressed 

 in the following form: 



(47) 

 2 F + Ax G v " 



'i-l.j' A^j 



where 



F = aa 2 , ,A. , . + (1 - 2a)a 2 .A. , + aa 2 , .A. , , 

 i,j+1 i,J+1 i,j i,j i,j-1 i,j-1 



2 2 



'a. , ,B. , . - a. . .B. , . 



lJ 2Ay 



2 2 



+ ,,( a i-i,>i B i-i,.i+i : a i-i,,i-i B i-i„i-i 



2Ay 



B = cc Vs sin 



cc Vs cos 



With the inclusion of the dissipative term, Equation 47 becomes 



23 



