122 



dispersion coefficient decreases from about 100 Gill's/day to 10 cm^/day at 

 distances of 90 and 275 m from the shoreline, respectively. At a distance 

 of 425 m, the tidally- induced dispersion coefficient would be about the 

 same as molecular diffusion for sodium chloride. 



The well-known Dupuit approximation is based on the assumption that 

 the hydraulic head is constant along any vertical line throughout the water 

 body and is therefore given by the elevation of the free surface. Strictly 

 speaking, although the Dupuit approximation allows only horizontal flow, it 

 provides meaningful solutions to a number of practical problems. 



The entire field of analytical and numerical modeling of groundwater 

 flows is based on Darcy's law which can be expressed as 



u = - V0 (8.3) 



in which u represents the three-dimensional velocity vector, ^ is the 

 velocity potential 



= K (E- - y) (8.4) 



V is the three-dimensional vector differential operator, and 



'»- ^H»*H"-^ K" ''■'' 



p is the pressure, y is the depth below a datum, K is the hydraulic 

 transmissivity of the medium, and i, j, k are the unit vectors in the x, 

 y, and z directions, respectively. The continuity equation for an 

 incompressible fluid is 



V'u = (8.6) 



which, when combined with Eq. 8.3, yields the Laplace equation in <)> 



v20 = (8.7) 



