Higher order analytical solutions of water table fluctuations in coastal aquifers

The groundwater response of coastal aquifers to tidal forcing is described by Laplace's equation coupled with the nonlinear phreatic-free surface boundary condition. Here we describe fluctuations in the water table using two small parameters, extending previous work by proposing an ansatz to compute higher order, semi-analytical solutions. The new solutions are compared with known lower order solutions. The relative difference between the linear solution and higher order solutions can reach up to 30% of the linear solution for shallow beaches. The new solutions exhibit a reduction in the over height of the groundwater fluctuations compared with the lower order solutions. In addition, the super elevation of the water table, both near shore and as the aquifer tends landward, is examined with the inclusion of higher order terms.