Solving The Problem Of Local Interface Upconing In A Coastal Aquifer By The Method Of Small Perturbations

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Abstract
The problem of determining the shape of the rising interface is presented in connection with the withdrawal of fresh water by shallow wells operating a short distance above the freshwater salt-water interface in a coastal aquifer. The exact equations required for solving the problem of the moving interface are developed. Because of the nonlinear nature of the boundary condition along the interface, a linearized approximate solution based on the method of small perturbations is described as a tool for obtaining an analytical solution for cases involving small deviations of the interface from some initial or average steady one. Both two and three-dimensional cases are considered. The range of validity of the analytical results is verified by means of experiments in a sandbox model.

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