-cirr ii~l ,9 =n-l ,o-,7r n-1 =n-l 

 Ti = 2.0 X 10 ^{[Ui(I,J)]2+[Vi(I,J)]2}2{u^(I^j)+V^(I^j)}^ 



and (59) 



= 1 = 

 Ti = 2.0 X 10"5{[V5|(I,J)]2+[U5|(I,J)]2}2{V5(I,J)+U5|(I,J)}, 



for even time steps. 



d) The coupling terms 



The coupling terms are coded based on the premise that the 

 energy transferred between modes due to coupling must be balanced. 

 The energy equations are formed by multiplying (37a, b) and (38a, b) by 

 Qg/D, gi/Zg, Qj^/^i, and eg\l/^, respectively, and thus the coupling terms 

 appear as 



-eg\('iQeV(Hi/D) (60a) 



-eg\i'eQiV(Hi/D) (60b) 



eg\('iQiV(Hi/D) (60c) 



eg«/'eQe^(Hi/D) (60d) 



For simplicity, consider a one dimensional channel in cartesian 

 coordinates as sketched in figure 4. The solid boundary is at point 

 1 while there are three possible conditions at point 7; i) a solid 

 boundary, ii) an open port, and iii) an interior point where the 

 interface intersects the bottom. Since the depth, and hence the 

 ratio H^/D, are defined at every field variable location the 

 gradients ["IxCHi/D)] are defined at midpoints between U and 4/ 

 locations (refer to points A, B, C, ... in Fig. 4). As an example, 



28 



