becomes quickly and uniformly mixed throughout the water column, the upstream 

 distribution will be proportional to the upstream distribution of salt water and the 

 downstream distribution will be proportional to the downstream distribution of 

 freshwater (Ketchum et al., 1952; Ketchum, 1955; Ketchum, 1969). 



One important consequence of these relationships is that the volume of water 

 available for the dilution of a pollutant is considerably greater in the estuary than it 

 would be in a river because of the participation of the salt water in the circulation. If, 

 for example, the mixed water moving seaward is 50 percent fresh and 50 percent salt, 

 it is clear that two volumes of the mixture must move seaward in order to remove the 

 one volume of river flow that isthe necessary net seaward transport across the cross- 

 section. Also, as the salt water content of the mixture increases, the volume that must 

 escape the system must also increase to carry one equivalent river flow seaward. 



A numerical example using Pritchard's ( 1969) method of calculation may serve to 

 clarify the process. It is presented in Table 6. This calculation is essentially a two- 

 layered box model in which the estuary is divided into a number of segments along its 

 length. The boundary between the upper and lower layers coincides with the bound- 

 ary between the surface layer having a net nontidal flow directed seaward and the 

 deeper layer having a net nontidal flow directed up-estuary. There is exchange be- 

 tween upper and lower layers by vertical eddy diffusion. The flux across any com- 

 plete cross-section of the estuary in both the upper and lower layers is derived from 

 the average salinity of these two layers assuming a steady-state salt distribution and 

 providing for continuity of salt and volume. The calculated flux is relative to the 

 flow of the river ( R) in a given unit of time, commonly a complete tidal cycle. For the 

 salinities arbitrarily chosen for Table 6. the seaward flux in the upper layer is three 

 times the volume of river flow and the up-estuary flux in the lower layer is twice the 

 river flow volume. The net flux is, as it must be in a steady-state distribution, equal to 

 the volume introduced by the river in the time period selected. 



In this example, both the upper layer and the lower layer are mixtures of fresh- 

 water and seawater, and the proportions of each, relative to offshore seawater, can 

 also be calculated from the salinity (Ketchum, 1951b). This permits the calculation of 

 the separate flux of salt water and freshwater in the system. There is a net flow of 

 freshwater out of the segment that is equal to the flow of river water in the period of 

 time selected. The flux of salt water seaward through the upper layer is exactly bal- 

 anced by the flux of salt water landward in the deeper layer. These two conditions. 



Table 6. Example of Calculation of the Horizontal Volume Flux, Relative 

 to River Flow R, Through a Cross-Section of a Hypothetical 

 Moderately Stratified Estuary 



Condition Upper Layer Lower Layer Net Flux 



Salinity % (S) 

 Volume flux (Q) 



Saltwater fraction (F s )§ 

 Freshwater fraction (F f )§ 



Saltwater flux 

 Freshwater flux 



*Q U = R(Si/Si - S u )and 



tQi = R (S u /Si - S u ) where Q is the flux, R is river flow, S is mean salinity of u the 



upper or 1 the lower layer (Pritchard, 1969). 

 §Relative to coastal, source seawater (a) of 32%o (Ketchum, 1 951 b);F s = Sx/a; 



Ff = 1 - F 8 = (a-Sx/a) where Sx is the mean salinity of the layer. 



77 



