A general analytical solution for groundwater fluctuations due to dual tide in long but narrow islands

Abstract

This paper develops a general mathematical model for describing head fluctuations in an aquifer of long but narrow islands subject to a dual tide effect. The upper boundary condition of the aquifer is represented by an equation combining the simplified free surface equation with a leakage term. Such an equation is considered as a general expression representing the upper boundary condition of a confined, unconfined, or leaky confined aquifer. The closed-form solution of the model represented by two series terms is developed by the direct Fourier method and finite Fourier sine transform. One of the series can reduce to a closed-form expression by means of contour integral and residue theorem. If the width of the island is very large, this solution gives the predicted head almost the same as that of the solution for an aquifer subject to a single tide effect. It is found that the presence of an upper aquitard produces significant vertical flow in the lower leaky confined aquifer even if the aquitard permeability is low. Neglecting such vertical flow may result in an overestimate of hydraulic head in the leaky confined aquifer. The attenuation factor and phase lag predicted from the present solution subject to the dual tide effect agree well with those estimated from 57 day head fluctuation data observed at Garden Island, Australia.