Tides as phase-modulated waves inducing periodic groundwater flow in coastal aquifers overlaying a sloping impervious base

This paper presents procedures for analysing the interactions between tidal waves and coastal aquifers overlaying a sloping impervious bed, using Boussinesq equation and wave equation. Fourier series solutions of a linearised Boussinesq equation are presented subject to a periodic boundary condition (BC). The periodic BC is a phase-modulated periodic solution of the wave equation which has been shown to satisfactorily simulate uneven twin peaks of semi-diurnal tides as observed in a study area on the east coast of Queensland, Australia. Numerical analyses show that the Fourier series solutions of Boussinesq equation subject to periodic BCs reveal two important features of the tidal waves. First, the tidal waves damp towards landward, and second, the half amplitude of the tide above the mean sea level is greater than that below it. While the first feature is clearly expected, the second feature is physically more meaningful and important, and is confirmed by the field data.