1 



A 



2- (EA 5- C 

 8x 8 x 



I QO ■ | I U) 



A = cross-sectional area 



Q = flow rate 



E = dispersion coefficient 



E includes the effects of upstream 

 bottom advection and tidal mixing. 

 If E is constant with distance and C 

 is constant with time (steady-state), 

 C is exponentially distributed, i.e. 

 C (x) = C o exp TV A ) + C (la). This 

 model has been useful in the study of 

 longitudinal salt distributions 

 (Simpson and Hammond unpublished; 

 Stommel 1953), but is of limited 

 use in problems where vertical 

 variations are important (Hansen 

 1967). This is the case for phy- 

 toplankton distributions in the 

 lower Hudson Estuary (Malone et 

 al. 1980) which is partially 

 mixed and characterized by two- 

 layered flow (Abood 1974). 



A simple model which incorpo- 

 rates vertical variation is the 

 two-dimensional box model (Prit- 

 chard 1969, Taft et al. 1978). 

 In this model the estuary is 

 divided into a series of longi- 

 tudinal segments and each segment 

 is divided vertically into two 

 layers at the boundary between up- 

 and down-stream net non-tidal 

 flow. Assuming that salinity 

 distribution approximates steady 

 state, and following the notation 

 of Pritchard (1969), the equations 

 defining transport are: 



Q ul = Qf s u/r s ii 



ui 



Q n = Qf s ui/f s H - s ui : 



Qvi 

 where 



Q 



Q ui+ r ^i 



(2) 



(3) 



ui 



upper layer downstream 

 flow at the i boundary 



Q.. . = lower layer upstream flow 

 at the i boundary 



S . ,S = upper and lower layer 



tidally averaged salini- 

 ties at i boundary 



Q f = freshwater flow 



Q . = vertical flow between 



.th , , . ,.th 

 i and (i + 1) 



boundary 



These equations are derived from 



continuity of salt (Q . S . = . 



ui ui Mi 



S ) and fresh water flow (Q = 



Q . - Q, . ) . Defining the mean 

 ui li 6 



salinity in the upper and lower 

 layer box between the i and 

 i + 1 boundary as 



M ui = ^ (S ui + l +S ui)' 



M n = ^ (s i 1+ i + s n> <*> 



continuity of salt in each box is 

 attained by the parameter E. (verti- 

 cal exchange) in 



Q . S . - (Q . , S . ,+ Q . M, . 



ui ui ui-1 ui-1 VI ll 



+ E. [M, . - M .]) = (5) 

 1 li ui 



Q 1 . S. . - (Q. . . S. . . + Q . M n . 

 li li li-l li-l vi li 



+ E. [M. . - M .]) = (6) 

 1 li ui 



169 



