A two-dimensional analytical solution of groundwater responses to tidal loading in an estuary and ocean

Previous studies on tidal dynamics of coastal aquifers have focussed on the inland propagation of oceanic tides in the cross-shore direction, a con®guration that is essentially one-dimensional. Aquifers at natural coasts can also be in ̄uenced by tidal waves in nearby estuaries, resulting in a more complex behaviour of head ̄uctuations in the aquifers. We present an analytical solution to the two-dimensional depth-averaged groundwater ̄ow equation for a semi-in®nite aquifer subject to oscillating head conditions at the boundaries. The solution describes the tidal dynamics of a coastal aquifer that is adjacent to a cross-shore estuary. Both the e€ects of oceanic and estuarine tides on the aquifer are included in the solution. The analytical prediction of the head ̄uctuations is veri®ed by comparison with numerical solutions computed using a standard ®nite-di€erence method. An essential feature of the present analytical solution is the interaction between the crossand along-shore tidal waves in the aquifer area near the estuaryÕs entry. As the distance from the estuary or coastline increases, the wave interaction is weakened and the aquifer response is reduced, respectively, to the one-dimensional solution for oceanic tides or the solution of Sun (Sun H. A two-dimensional analytical solution of groundwater response to tidal loading in an estuary, Water Resour Res 1997;33:1429±35) for two-dimensional non-interacting tidal waves. Ó 2000 Elsevier Science Ltd. All rights reserved.