2 F + Ax G Ax D .„_. 



a i-i,j ~- a. ; . + 1~— (48) 



' J 1-1, J 1-1, J 



where D* represents the finite difference form of the dissipation term on 

 the right-hand side of Equation 46. Reiterating, the dissipation term is an 

 average value along the wave path. The wave path is determined by the local 

 wave angle at the position i-1,j which has already been computed. There- 

 fore, the average along the path is an average of information at cell i— 1 , j 

 and another cell whose position is denoted by ikey,jkey . The procedure used 

 for determining the location of this cell will be presented later. 

 41. The term D can be written in finite difference form as 



D 



a cc I Vsl ) ., ., + (a cc I Vs I ). , . 

 v g 1 '/lkey.jkey \ g 1 '/i-I./i 



(49) 



-(fcj 



where 



2/y h cc Ivsl.. ., + y h cc l Vs | . . . 



I [ g 'ike.y./ikey gl 'i-1,,i 



5 _ i-1 ? j + h ikey T , i ke y 



With some algebra, Equation 48 can be reorganized so that the amplitude func- 

 tion at the position i— 1 , j only appears on the left-hand side of the equa- 

 tion. Therefore, the energy equation inside the surf zone can be numerically 

 solved using the same procedure which was used to solve it outside the surf 

 zone. 



42. The location of the cell denoted ikey,jkey is found using the 

 following procedure. "Areas of influence" are determined by extending lines 

 from the center of the cell i— 1 , j to the midpoints between the surrounding 

 cell centers (Figure 3). Angles are computed from the x-axis to these radial 

 lines. The local wave angle calculated at cell i-1,j is compared to each of 

 these angles in order to determine the nearest, prior cell along the wave 

 path. For example (refer to Figure 3), if the local wave angle is greater 

 than 6 2 but less than e. , then cell i,j+1 is the cell of influence and 

 ikey = i and jkey = j+1. 



43. A flow chart describing the wave height computation is shown in 



24 



