Two-dimensional analytical solution for tide-induced watertable fluctuations in a sandy rhythmic coastline

Modelling of tide-induced watertable fluctuations in coastal unconfined aquifers has, for many years, been based on the assumptions of one-dimensional shallow flow and a vertical beach face. This approach is based on the Boussinesq equation, neglecting variations in the coastline and beach slope. Here, a closed-form analytical solution for a two-dimensional unconfined coastal aquifer, taking account the sloping and variable coastline, is derived. In the appropriate limits, this new solution reduces to the vertical beach, one-dimensional solution. The effects of different beach slopes and the coastline variability for a typical sandy beach environment are investigated. The results indicate that both the coastline shape and beachface slope are important parameters affecting the solution for tide-driven coastal groundwater fluctuations.