SEAWATER-FRESH-WATER INTERFACE IN A STRATIFIED AQUIFER OF RANDOM PERMEABILITY DISTRIBUTION

We consider the problem of a sharp interface between salt and fresh wa ters in an aquifer of spatially variable permeability. We assume a lay ered structure, with permeability a stationary random function of the vertical coordinate, of given mean and two point covariance. The flow is shallow and it obeys the Dupuit assumption. We derive an exact anal ytical solution of two-dimensional steady flow of fresh water in a con fined aquifer, with salt water at rest. The mean interface shape is a Dupuit parabola, for a constant effective permeability equal to the ar ithmetic mean of the random permeability. The variance of the interfac e coordinate, and particularly of the toe, depends on the permeability variance and integral scale. The uncertainty of the interface locatio n can be large. We also investigate the uncertainty of the discharge o f a coastal collector, for a given depth of the upconed interface. We also determine, by using conditional probability, the impact of measur ement of the interface depth in a given cross-section on the reduction of the uncertainty of its position. The second case is the generaliza tion of the solution by Keulegan (1954, National Bureau of Standards R eport, Department of Commerce, Washington, DC) of unsteady flow that r esults from an abrupt removal of a thin vertical partition between sal t-and freshwater bodies. The mean interface is similar to that prevail ing in a homogeneous medium, i.e. a rotating line whose slope approxim ately corresponds to the permeability arithmetic mean. The uncertainty affecting the interface position is of a smaller extent than that in steady flow. (C) 1998 Elsevier Science B.V.