SECT. 3] ESTUAK1ES 317 



tide), the average distribution of fresh and salt water within an estuary could 

 be calculated. 



Ketchum's empirical theory was formalized by Arons and Stommel (1951) 

 into a mixing length theory of tidal flushing in which the characteristic length 

 was associated with the horizontal tidal excursion. Stommel (1953) later 

 questioned the acceptability of associating the mixing length with the tidal 

 excursion and suggested that the coefficient of turbulent diffusion should be 

 computed from the observed distribution of salinity within the estuary under 

 consideration. 



Preddy (1954) pointed out that the dispersal of a volume of water due to 

 tidal mixing might be represented by a distribution curve appropriate to each 

 point in the estuary. He represented these curves by simplified asymmetrical 

 distributions involving two constants which could be determined from the 

 observed salinity distribution. In applying his method to the Thames Estuary, 

 he demonstrated that the dispersion of a unit of water varies with position 

 along the estuary and at each position is greater to seaward than headward. He 

 verified his method by successfully predicting changes in the salinity distribu- 

 tion resulting from the changes in river flow. 



Gameson, Hall and Preddy (1957) applied Preddy 's method to estimating 

 temperature changes in the Thames which would follow an alteration in the 

 amount of heat discharged into the estuary. 



Dorrestein (1960) has proposed a numerical approach to the dispersion of an 

 introduced contaminant in an estuary, somewhat similar to Preddy's method. 

 However, Dorrestein has devised a practical technique for computing numerical 

 solutions to the difference equations for the non-stationary distribution of 

 concentration by means of matrix calculus. 



The foregoing methods of computation assume that the significant process 

 which maintains a steady state of salinity in the presence of a net advective 

 flow of fresh water from the river is eddy diffusion along the longitudinal 

 salinity gradient from the sea. There remains the question whether, in such 

 cases, the possibility of advective transport of salt should be entirely neglected. 

 The studies of Inglis and Allen (1957) on the distribution of mud in the Thames 

 Estuary indicate an observable net upstream flow along the bed of the river to 

 a point where the average salinity is as low as 5% . The fact that this upstream 

 flow could not be reproduced in models operated with fresh water throughout 

 confirms that it is not associated with the geometry of the estuary nor the dis- 

 persal effect of the tide. It is clear that, in studies such as those associated with 

 silting, the dynamic effect of the salinity distribution is significant, and over- 

 simplification of the mechanism of the estuary will conceal important factors 

 in flushing. 



6. Dynamics of Estuaries 



In this section some of the principles of estuarine circulation described 

 above will be expressed more formally in mathematical terms. For this purpose, 



