SECT. 3] ESTUARIES 323 



usual approach is to treat turbulent diffusion as analogous to molecular diffu- 

 sion, and make substitutions of the type 



<u' x s>)= -K x £, (14) 



where K x is the longitudinal eddy diffusivity. There is no adequate theoretical 

 basis for determining the spatial and temporal variations in the eddy diffusivity. 

 The usual approach is to determine empirically the eddy coefficients for a given 

 environmental situation, using the observed distributions of some conservative 

 property, and to use these coefficients in predicting the distribution for other 

 conditions. Thus the one-dimensional form of (13), which applies to a sectionally 

 homogeneous estuary, has been solved numerically for the temporal and 

 spatial distributions of an introduced contaminant, using the longitudinal 

 diffusivity computed from the steady-state distribution of salinity. A similar 

 treatment has been used to predict the distribution of salinity in a sectionally 

 homogeneous estuary under varying conditions of fresh-water inflow. 



Another approach to the mathematical description of the distribution of 

 salinity or of an introduced contaminant in an estuary involves the segmenta- 

 tion of the estuary into sections within each of which the concentration is 

 assumed to be constant but different from that found in adjacent segments. 

 A difference equation is developed involving so-called "exchange coefficients", 

 which express the fractional rate of exchange of water between adjacent 

 segments. These exchange coefficients are determined from observed distribu- 

 tions of salinity, and the relationship utilized for predicting purposes. 



These engineering approaches are of considerable practical value. However, 

 they remain completely unsatisfactory from the standpoint of actually ex- 

 plaining the mechanisms controlling the distribution of properties in an estuary. 

 An adequate understanding of the eddy-flux terms is required. The observa- 

 tional data necessary as a basis for such understanding necessitate observational 

 techniques different from those now in common use. 



One observational approach to the problem is the direct measurement of 

 turbulent fluctuations in velocity and salinity. Some progress has been made 

 on the instrumentation for such observations. A second approach involves 

 direct observation of the diffusion of an introduced tracer substance. Significant 

 advances in detection methods and observational techniques for such direct 

 measurements of diffusion in estuarine waters are reported by Pritchard and 

 Carpenter (1960). 



References 



Abbott, M. R., 1960. Boundary layer effects in estuaries. J. Mar. Res., 18, 83-100. 

 Arons, A. B. and H. Stommel, 1951. A mixing length theory of tidal flushing. Trans. Amer. 



Geophys. Un., 32, 419-421. 

 Bousfield, E. L., 1955. Some physical features of the Miramichi estuary. J. Fish. Res. Bd. 



Canada, 12, 342-361. 



