2 . A = 7 — - — (aa 2 , ,A. , , + (1 - 2a)a. .A. . + aa. , ,A. , .) 



^(-Li.j*i b i-,,j*i - -Li.j-i-i-,,^1? 



(1-W)Ax 

 2Ay 



( a i,j + 1 B i,j + 1 " a ?,j-1 B i,J-l)j 



This equation can be solved for the wave amplitude function, and subsequently 

 the wave height, at the location i-1,j . The remainder of this section de- 

 scribes the procedure used to solve the set of approximate Equations 14, 21, 

 and 26. 



23. Model input (described in detail in Part IV) includes values of the 

 deepwater height H Q , direction 9 , and period T of waves to be simu- 

 lated. It also includes specification of the bottom bathymetry throughout the 

 grid. The wave number, which is related to the wave period and the local 

 water depth through the dispersion relation, is computed at every cell. Wave 

 number is used as an initial guess for the magnitude of the wave phase func- 

 tion gradient. The wave celerity c and the group velocity c are func- 

 tions of the wave period and wave number. Therefore these variables can be 

 calculated at each cell. 



24. From Snell's law, 



sin 9 

 sin 8 _ o /p„x 



c c 

 o 



where c Q is the deepwater wave celerity (defined to be gT/2Tr ), an estimate 

 of the local wave angle is calculated everywhere. This estimate assumes that 

 the bottom contours are parallel with the y-axis. If the bottom bathymetric 

 contours make a known nonzero angle with the y-axis, a better first guess for 

 the wave angles can be computed. The new approximation is 



/sin (9 - 9 ) 

 - sin" 1 2 5_| + e (28) 



15 



