An analytical solution of the tide-induced groundwater table overheight under a three-dimensional kinematic boundary condition

Abstract

Time averaged groundwater table above the mean sea level has been observed in unconfined coastal aquifers. Several theoretical solutions were presented to investigate the groundwater table overheight (super-elevation) in response to tidal oscillations. Nevertheless, previous analytical solutions are generally limited to Dupuit-Forchheimer assumptions or a two-dimensional free surface model. In this paper, we introduced a more general condition that a three-dimensional kinematic boundary condition is considered. An exact analytical solution of the groundwater table overheight under the multi-tidal constituents was derived using the Fourier transform method. The solution shows the local groundwater table overheight is related to the mean aquifer thickness, tidal amplitude, damping coefficient as well as its positions in sand beaches. In addition, the analytical solution illustrates the simple linear superposition is not applicable to the multi-tidal components condition, whose groundwater table overheight becomes weak due to the non-linear effect of the three-dimensional kinematic boundary condition. In addition, concentrations were focused on the time averaged total flux density illustrating the groundwater exchange occurs both in the shore normal and shore parallel directions, which however is missing in the previous two-dimensional solution. Further cognitions on the groundwater circulation mechanism were also achieved, which originates from the large tidal amplitude region and fans out towards the small tidal amplitude region. These new findings are of great importance to extend our understandings of the groundwater hydrodynamics in unconfined coastal aquifers.