wave approximations of small vertical accelerations and a homogenous fluid 

 yield the following vertically integrated (depth-averaged) two-dimensional 

 equations of continuity and momentum: 



Continuity 



I? + h (>■« * h <"« ■ " "' 



Momentum 



1/2 

 9u , 9u , 3u ^ ^ 8 . N _L 8" /- 2 , 2. 



-^&^0h^^'° ^^' 



1/2 

 3v _^ 3v _^ 9v , ^ , 9 , ^ J. gv . 2 2 ' 



9i ■" " 9l ^ ^ 97 ^ '" "" ^ 97 ^' " "a^ ■" ^ ^" "" ^ ^ 



where 



\9x 9y / ^ 



n = water surface elevation above datum 



t = time 



u,v = velocities in the x- and y-directions 



d = n + h, the total water depth 



h = local still-water depth 



R = rate of water volume change in the system due to rainfall or 

 evaporation 



f = Coriolis parameter 



g = acceleration due to gravity 



C = Chezy coefficient for bottom friction 



e = eddy viscosity coefficient 



16 



