Two-dimensional approximation for tide-induced watertable fluctuations in a sloping sandy beach

Abstract

The prediction of watertable fluctuations in a coastal aquifer is important for coastal management. However, most previous approaches have based on the one-dimensional Boussinesq equation, neglecting variations in the coastline and beach slope. In this paper, a closed-form analytical solution for a two-dimensional unconfined coastal aquifer bounded by a rhythmic coastline is derived. In the new model, the effect of beach slope is also included, a feature that has not been considered in previous two-dimensional approximations. Three small parameters, the shallow water parameter ( ε), the amplitude parameter ( α) and coastline parameter ( β) are used in the perturbation approximation. The numerical results demonstrate the significant influence of both the coastline shape and beach slopes on tide-driven coastal groundwater fluctuations.