310 CAMERON AND PRITCHARD [CHAP. 15 



is relatively much larger than the corresponding flow in the salt-wedge estuary, 

 and compensating flow in the deep water is also greater. 



The broader excursions of the turbulent elements resulting from the more 

 vigorous activity cause a more extensive flux not only of salt but also of 

 momentum. Instead of being localized at or near the interface, the eddy stresses 

 will tend to extend throughout the layers from the bottom to the surface. A 

 more complicated distribution of pressure gradients must be. established if the 

 estuary is to maintain a steady state from tidal cycle to tidal cycle. Relatively 

 horizontal pressure surfaces in the deeper water were associated with the salt- 

 wedge estuary. Here, in contrast, pressure surfaces in the deeper layer must 

 slope downward toward the head to overcome the frictional effect of turbulent 

 motion on the compensating headward flow. 



In the upper layer, pressure surfaces must slope downward toward the sea. 

 This variation with depth in the inclination of the pressure surfaces is brought 

 about by the type of mass distribution resulting from the more intensive 

 mixing. 



It is commonly considered that the increased circulation that occurs in 

 estuaries of moderate tidal mixing is powered by the increased potential energy 

 of the system which results from the vertical mixing of fresh and salt water. 

 What we are suggesting here is rather that the mixing process of the tide leads 

 to the establishment and maintenance of stronger horizontal gradients of 

 density within the estuary than would occur without tidal mixing. These 

 horizontal gradients of density in turn permit horizontal pressure gradients of 

 magnitude and distribution sufficient to maintain the relatively higher veloci- 

 ties in the presence of increased eddy frictional force. In other words, it is tidal 

 mixing that promotes and permits the required distribution of potential 

 energy within the estuary. 



In the preceding paragraphs we have referred to the mean slope of the 

 pressure surfaces over several tidal cycles. Superimposed on these mean slopes 

 there will occur oscillating variations in slope associated with the flood and ebb 

 of the tide. It is generally assumed that the variations in slope due to the tide 

 are symmetrically distributed about the mean and that they are suppressed in 

 the averaging process. To date it has also been assumed that the time variation 

 in the tilt of the pressure surfaces is independent of depth and reflects the 

 variation in slope of the water surface of the estuary. This assumption has per- 

 mitted a concentration of attention upon the vertical gradient of slopes within 

 the estuarine water and its association with the dynamics of the "mean" or 

 "net" motion. 



Recently, the averaging process has received more critical attention. There 

 has been an increased appreciation of the nature of the non-linear inertia terms 

 in the equation of tidal motion. Inasmuch as they involve products of the 

 velocities, they do not average out over a tidal cycle. Thus, Pritchard (1956) 

 has examined the effect of the non-linear term resulting from a variation in 

 tidal excursion with distance along the estuary. Stewart (1957) has called 

 attention to the effect of the curvature of the tidal channel in giving rise to a 



