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

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.