A two-dimensional analytical solution of groundwater response to tidal loading in an estuary

A two-dimensional transient groundwater flow equation for a confined nonleaky aquifer is served analytically with an estuary tidal-loading boundary condition. The amplitude and phase of the tide varies with position and time, respectively. These variations, called the ''damping coefficient,'' for amplitude, and ''separation constant,'' for phase along the coastline, are considered in the analysis. The solution presented is more advanced than the traditional one-dimensional analytical solution with a one-dimensional tidal-loading boundary condition. The damping coefficient and separation constant in the application study are obtained from the harmonic analysis of the observed tidal level in Apalachicola Bay, Florida. The analytical solution is compared to a two-dimensional finite difference solution. A numerical simulation illustrates the response of piezometric head to tidal loading. The piezometric head and phase from both solutions match closely. The analytical and numerical solutions show that a piezometric head along both sides of the estuary can be predicted given a tidal elevation at the entry of an estuary. The fluctuation of piezometric head in response to tidal loading diminishes rapidly inland and diminishes slowly along the coastline of an estuary. There are also obvious phase shifts associated with spatial variations as the wave propagates.