New Perturbation Solution for Tidal Water Table Fluctuations in Unconfined Aquifers with Sloping Beaches

Tidal water table fluctuations are important characteristics of coastal unconfined aquifers and have been linked to beach profile changes. Mathematical models of such fluctuations based on the Boussinesq equation are subjected to a moving boundary condition induced by the beach slope. Approximate analytical solutions of these models have been previously derived using the perturbation method based on the perturbation variable ɛ=Acot(φ)\sqrt{neω/(2KD) (A and ω are tidal amplitude and frequency, respectively; φ is the beach angle; K, ne and D are the hydraulic conductivity, effective porosity and mean thickness of the aquifer, respectively). The applicability of these solutions is limited by the condition of ɛ < 1, which may not hold at coasts with relatively flat beaches. Here we present a different perturbation approach using a new perturbation variable β=ɛ/(1+ɛ), which by definition is less than unity. Comparison of the new solution with previous analytical and a numerical ("exact") solution shows significant improvement of the new perturbation approach.