2.8 External Mode 



In the present study, numerical computation of the internal mode, which 

 is governed by the slower baroclinic vertical flow structure dynamics, is 

 separated from the computation of the vertically-integrated variables 

 (external mode), which are governed by the fast barotropic dynamics. This 

 so-called "mode splitting" technique resulted in significant improvement of 

 the numerical efficiency of a three-dimensional hydrodynamic model for Lake 

 Erie (Sheng et al., 1978) and was detailed in Sheng and Lick (1980). 

 Basically, it allows for computation of the three-dimensional flow structures 

 with minimal additional cost over computation of the two-dimensional flow with 

 a vertically-integrated model. 



Vertically-Integrated Equations 



The external mode, as described by the water level (c) and the 

 vertically-integrated mass fluxes (U and V), is governed by the following 

 equations: 



n 



9U 



3V 



Pj^3X Py3y 



(2.36) 



lU = . JL li + V - ^ I -^ ( ^ 



3t 



U^ 3X 





Vyiy 



m 



^do-^-^ 



pudX p„3 



-■U 



pdo + op 



H 3Pc 



3X 



Hdo 



+ T 



sx 



bx 



X 



H (H.D.)„ do = - — 7^ + D^ 

 ^ Vy^ 3x X 



(2.37) 



37 



