SECT. 3] ESTUARIES 321 



vanish, and for steady-state conditions in an embay ment with a progressive 

 tidal wave, equation (6) would be given by 



This relationship shows that even in the absence of any density gradients, 

 there would occur a mean slope of the surface of the embayment related to the 

 longitudinal variation in tidal-current amplitude. 



In an estuary, the density distribution is not uniform. The distribution of 

 temperature and salinity can be utilized to compute the density distribution 

 which, when employed in the hydrostatic equation, allows the determination 

 of the pressure gradient relative to some pressure surface — for example, water 

 surface of the estuary. Left undetermined is the absolute mean slope of the 

 water surface. However, if the term d((u' ' z u' ' x y)jdz is the only eddy stress of im- 

 portance in (6), this equation can be integrated with depth from the surface to 

 the bottom of the estuary. On the basis of boundary layer theory, reasonable 

 estimates of the boundary values for the eddy flux of momentum can be made. 

 Such a procedure allows the determination of the mean absolute slope of the 

 water surface, since this term would be constant in the vertical integration of 

 equation (6). Pritchard (1956) used the observed distribution of velocity and 

 density in the James River estuary in (6) to compute the absolute longitudinal 

 slope of the pressure surfaces. Using (7) in a similar manner, he determined the 

 lateral slope of the pressure surfaces. This work showed that, in a partially 

 mixed estuary, the water surface has a mean slope downward toward the sea 

 and also downward to the left of an observer facing the sea. At about mid- 

 depth the pressure surface is level in both the longitudinal and lateral direc- 

 tions, but in the deeper layers the pressure surfaces slope in the opposite 

 direction to the slope of the water surface. 



The estuary of the River Thames, in England, is reported to be vertically 

 homogeneous in density. There is observed in this estuary, however, a net 

 motion directed from the sea landward on the bottom, and a net flow directed 

 seaward in the upper layers. Abbott (1960) argues that the non-linear tidal 

 current terms in the mean longitudinal equation of motion, coupled with 

 bottom friction, would produce just the mean flow observed. His argument 

 should be weighed against the failure by Inglis and Allen (1957) to produce 

 experimentally upstream bottom flow in a fresh-water hydraulic model of the 

 Thames. 



In the descriptive paragraphs it was pointed out that in certain embay ments, 

 tributary to large estuarine systems, a three-layered net flow pattern is ob- 

 served, with inflow from the adjacent estuary to the embayment at both the 

 surface and bottom, and outflow at mid-depths. We would suspect that in such 

 an embayment the pressure surfaces would slope downward toward the head 

 of the embayment at both the surface and bottom, and in the opposite direction 

 at mid-depth. Level pressure surfaces would then occur at two depths, one at 

 the boundary between the surface layers and the mid-depth layers, aud the 



