An analytical solution for tidal fluctuations in unconfined aquifers with a vertical beach

Abstract

The perturbation technique has been commonly used to develop analytical solutions for simulating the dynamic response of tidal fluctuations in unconfined aquifers. However, the solutions obtained from the perturbation method might result in poor accuracy for the case of the perturbation parameter being not small enough. In this paper, we develop a new analytical model for describing the water table fluctuations in unconfined aquifers, based on Laplace and Fourier transforms. In the new approach, the mean sea level is used as the initial condition and a free surface equation, neglecting the second-order slope terms, as the upper boundary condition. Numerical results show that the present solution agrees well with the finite different model with the second-order surface terms. Unlike Teo et al.'s (2003) approximation which restricts on the case of shallow aquifers, the present model can be applied to most of the tidal aquifers except for the very shallow one. In addition, a large-time solution in terms of sine function is provided and examined graphically with four different tidal periods.