Applicability of analytical solutions to tidal propagation in circular islands

Abstract

The propagation of tides into coastal aquifers is an important phenomenon in the migration of coastal contaminants, for the representation of shoreline boundary conditions in regional-scale groundwater models, and for the estimation of aquifer properties based on tidal amplitude attenuation and/or phase increase. In this study, an analytical solution to the propagation of tidal fluctuations in a radial flow field, applicable to circular islands, is compared to the existing straight-coastline (“Ferris”) solution. The analytical solution is compared to numerical simulation (using SEAWAT) of a simple-harmonic ocean tide and its propagation within a circular island. This represents the first attempt to combine a previous correction that allows SEAWAT to simulate axisymmetric flow and a modification to SEAWAT to create tidal boundary conditions. Bench testing the analytical solution against the numerical model confirms the numerical approach. The circular-island solution is compared to the Ferris solution in terms of tidal amplitude decay and phase shift. Whereas amplitude decay from the Ferris solution is valid only for near-shore locations within circular islands, the Ferris solution produces reasonable phase lag estimates for typical aquifer diffusivities and for most locations within circular islands. By comparing the Ferris and circular island solutions, we propose a correction factor to the Ferris solution that allows it to be applied in circular boundary settings. This extends the application of the widely applied Ferris solution to a broader range of situations.