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8.3 PHYSICAL PRINCIPLES AND SOLUTIONS TO IDEALIZED PROBLEMS 

 8.3.1 General 



A simple hydrostatic analysis of the balance between a freshwater 

 aquifier meeting a saline water body yields the Ghyben-Herzberg principle 



z £— h (8.1) 



Ps - Pf 



as illustrated in Fig. 8.2. The above relation applies for a distinct 

 fresh- saltwater interface. However, field measurements have proven 

 definitively that the transition between salt and fresh water is quite 

 gradual with mixing occurring over this transition zone, see Fig. 8.3. The 

 principal cause of the gradual transition, which can be interpreted as 

 dispersion, is the movement of this interface back and forth due to the 

 relatively short period astronomical tide components and also the longer 

 term oscillations due to seasonal variations in replenishment by rainfall 

 and the still more infrequent droughts. During the saltwater advancement 

 and retreat, some salt water is left in the interstices. This is the 

 so-called convective mode. The mixing with the retained fresh water occurs 

 by more slowly occurring molecular diffusion. Experiments have been 

 conducted which demonstrate that the dispersion due to ocean tides can be 

 expressed as 



D = 4MA/to (8.2) 



where M is a parameter with dimensions of length and A and t^ are the 

 horizontal amplitude of tidal motion and period, respectively. Laboratory 

 studies have been shown that the parameter, M, increases with the 

 uniformity of the stratum and can range from 0.063 cm to possibly as high 

 as 2.8 cm for very uniform sand. Methods employing numerical models 

 combined with Taylor's hypothesis relating the dispersion coefficient 

 tensor, the pore water velocity fluctuations and the Lagrangian time scale 

 tensor have been used to predict anisotropic dispersion coefficients (e.g., 

 Fattah and Hoopes , 1985; Chin, 1986). Based on realistic values of tidal 

 and ground permeability characteristics, it can be shown that the 



