Tide-induced groundwater level fluctuation in coastal aquifers bounded by L-shaped coastlines

Abstract

This paper presents an analytical solution to describe tidal groundwater level fluctuations in an aquifer bounded by two water-land boundaries that form a right angle. The aquifer configuration can represent the situation of a right-angle comer in an island when the tidal boundaries are the same along both boundaries, or the estuary situation if the amplitude damps with distance along one boundary (river) and the amplitude along the other boundary (sea) does not change spatially. The two-dimensional flow equation subject to periodic boundary conditions is changed into a time-independent elliptic problem using complex transform. The elliptic problem is then solved using the Green's function method. Li et al. [2000] obtained a nonperiodic solution to the same problem with an additional hypothetical initial condition. Their solution includes a time-dependent integral. The solution presented here is a significant improvement over theirs in the sense that the solution is periodic and computationally efficient since the integral involved is independent of time. An approximate solution without integral is also derived. An error analysis and a case study in Hong Kong demonstrate that the approximate solution is adequate for most field problems.