Exact versus Dupuit interface flow in anisotropic coastal aquifers

Abstract

The Dupuit solution for interface flow toward the coast in a confined aquifer is compared to a new exact solution, which is obtained with the Hodograph method and conformal mapping. The position of the toe of the interface is a function of two dimensionless parameters: the ratio of the hydraulic gradient upstream of the interface where flow is one-dimensional over the dimensionless density difference, and the ratio of the horizontal hydraulic conductivity over the vertical hydraulic conductivity. The Dupuit interface, which neglects resistance to vertical flow, is a very accurate approximation of the exact interface for isotropic aquifers. The difference in the position of the toe between the exact and Dupuit solutions increases when the vertical anisotropy increases. For highly anistropic aquifers, it is proposed to add an effective resistance layer along the bottom of the sea in Dupuit models. The resistance of the layer is chosen such that the head in the Dupuit model is equal to the head in the exact solution upstream of the interface where flow is one-dimensional.