New approximation for free surface flow of groundwater in coastal aquifers

Free surface flow of groundwater in aquifers has been studied since the early 1960s. All previous investigations have been based on the Boussinesq's equation, which is derived from the non-linear kinematic boundary condition. In fact, the Boussinesq's equation is the zeroth-order equation in the shallow water expansion. The principle of the shallow water expansion is the mean thickness of aquifer (D) is small compared to the reference length, which normally is the linear decay length (L). In this study, we re-examine the mechanism of free surface flow of groundwater. In the new approximation, the assumption of shallow water is removed. With experimental data, the new model provides a better prediction of watertable level than the conventional shallow water expansion. Numerical examples also indicate the applicable range of the conventional shallow water expansion.