322 CAMERON AND PRITCHARD [CHAP. 15 



second at the boundary between the mid-depth layers and the bottom layers. 

 Use of the mean longitudinal equation of motion with the observed distribution 

 of velocity and density for one such embayment, Baltimore Harbor, confirms 

 this mean distribution of pressure. 



7. Kinematic Description of the Distribution of Properties in an Estuary 



The mathematical relationship expressing the conservation of a water-borne 

 constituent can be developed from the equation of continuity. We designate 

 the local instantaneous concentration of some conservative property of the 

 estuary, such as salt concentration, by s, and obtain the following differential 

 equation 



8s 8u x s duyS 8u z s 



8t 8x 8y 8z 



(11) 



where the molecular diffusion terms are omitted. Again, it is not possible to 

 treat this instantaneous relationship. As with the velocity components, we 

 consider the instantaneous concentration s to be composed of three terms : a 

 time mean concentration over one or more tidal cycles ; a term which varies 

 sinusoidally with the tidal period ; and a turbulent deviation term. Hence, 



s = s+Su + s'. (12) 



The major cause of fluctuations of tidal period in the local salt concentration 

 is the advection of the longitudinal salinity distribution with the longitudinal 

 component of the tidal current. The velocity component U x and the salinity 

 term Su would then be approximately 90° out of phase, and cross-products 

 involving these two terms would disappear from the mean form of (12). Using 

 arguments similar to those presented in the development of (6) and (7), we 

 obtain for the time mean of (11) over a tidal period 



8s 8u x s 8u y s 8u z s 8 8 d , 



j t = ■■^r-^-^r-te< u * s >-y y < u > s >-irz< u * s >- (13) 



For each of the estuarine types described in the earlier paragraphs, a different 

 set of terms will dominate (13). Thus, at the interface in a salt-wedge estuary 

 the upward breaking of the interfacial waves can be considered as a net vertical 

 advection, and the salt balance would be maintained primarily by the longitu- 

 dinal and vertical advective terms in the equation. In the upper, seaward- 

 flowing layers of such an estuary the vertical eddy flux of salt would also be 

 important. Pritchard (1954) showed that in a partially mixed estuary the 

 terms related to the longitudinal advective flux and the vertical eddy flux are 

 dominant, with the vertical advective flux making a significant but lesser 

 contribution. The other terms in (13) appear to be negligible. In a vertically 

 homogeneous estuary only the horizontal terms would be significant. 



There is very little basis for deciding on the form of the eddy-flux terms. The 



