latter accumulates in the upper zone where the velocity increases to 

 seaward in direct proportion to the increase of sea-water content, and 

 inversely as the cross-section area of the upper zone. 



The seaward salinity gradient originates in the turbulence function 

 and is maintained by the displacement flow. The latter is limited to 

 the depth of the boundary, which must therefore be a minimum 

 potential surface and cannot be altered by forces within the system. 

 The upper and boundary zones are everj-^where less dense than the lower 

 zone, therefore any change of level will invoke local accelerations to 

 restore the position of minimum potential energy. The difference in 

 level between extremes of this zone in the data cited in Fig. 4 would be 

 of the order of 7 centimetres, which is within the limits of accuracy of 

 the observations. 



Displacement 



From the preceding discussions it may be realized that at equilibrium 

 the fresh-water outflow must be displaced seaward at a rate equal to its 

 supply, therefore it must be possible to evaluate the seaward movements 

 in the upper zone and the degree of mixing in terms of the discharge of 

 the parent river. 



Some proportion of the fresh and sea water in any limited region of 

 the upper zone is displaced by like amounts entering the region in a 

 limited time-interval. Evidently the proportion of fresh water displaced 

 is the same as the proportion of sea-water displaced, otherwise one or 

 other of the components would accumulate. Therefore displacement ma}^ 

 be quantitatively defined as the proportion of water in any limited region 

 that is replaced by new water in one complete tide-cycle. Displacement 

 may then be evaluated from an analysis of the fresh-water distribution : 

 consider an area (A) in which the depth of the upper zone (D) contains 

 a proportion of fresh water (C), into which the rate of fresh water 

 discharge is (Q) during the time of a tide-cycle (T). Then the displace- 

 ment of fresh water (r) is the ratio of the volume of fresh water entering 

 the region (OT) to the volume of fresh water already in the region 

 (A C D) 



_ _QX 



^ ~ ACD 



This expression is exact and implies an absolute knowledge of the 

 factors. However, when observing the natural state it is usually 

 necessary to make interpolations and approximations in the values. 



The depth of the upper zone may be determined as the intercept of 

 the lower and boundary gradients (Fig. 4). The proportion of fresh 

 water in the region is the ratio of the area bounded by the salinity 

 curve, the surface, and the salinity ordinate intercepting the point 

 defining the depth of the boundary, to the product of this salinity and 

 depth. These quantities may be interpolated with reasonable accuracy 

 from suitable salinity observations, and usually the runoff may be 

 observed directly. Therefore the equation can be solved in any region 

 where the boundaries can be defined. 



Relation to Runoff 



The relations of these quantities to the discharge of the parent 

 stream are shown in Fig. 5, from the studies in the simple system in 

 Alberni Inlet(l). 



276 



