Simulating seawater intrusion in aquifers using the modified Fokker-Planck equation and Boussinesq equation subject to phase-modulated tidal waves

Abstract

This paper is concerned with the interactions between periodic tidal waves and coastal aquifers. The analysis is based on a set of equations governing the hydrodynamic interactions near coastal regions consisting of a modified Fokker-Planck equation for modelling the transport of salts, a Boussinesq equation for groundwater flow and a wave equation for tidal waves. The modified Fokker-Planck equation is featured with a time- and scale-dependent dispersivity, and solutions of the Boussinesq equation are obtained subject to phase-modulated tidal waves as the boundary condition which is a solution of the wave equation. The phase-modulated periodic solution of the wave equation is shown to satisfactorily simulate the uneven twin peaks of semi-diurnal tides. Fourier series solutions of the Boussinesq equation subject to periodic boundary conditions reveal that the tidal waves damp towards land, and the half amplitude of the tide above the mean sea level is greater than that below it. Seawater-freshwater interface is also analysed using the modified Fokker-Planck equation.