Zhiyao Song, Zhuo Zhang, Ling Li


Based on a liberalized one-dimensional Boussinesq model and the previous study results, this paper provides two experience solutions to quantify the tidal groundwater overheight behind arbitrary sloping beaches. One solution is obtained with an asymptotic matching method advanced by Guo, and the other solution is origined by the analytical solution as perturbation parameter less than unity, the errors of both solutions compared with numerical solution are small and acceptive for the application.


Coastal aquifer; Tidal watertable; Boussinesq equation; logarithmic matching

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Church, T. M., 1996, A groundwater route for the water cycle. Nature, 380, 579–580.http://dx.doi.org/10.1038/380579a0

Guo, J., 2002, Logarithmic matching and its applications in computational hydraulics and sediment transport. J. Hydr. Res., 40(5), 555-565.http://dx.doi.org/10.1080/00221680209499900

Li, L., D. A. Barry, F. Stagnitti, J.-Y. Parlange, and D.-S. Jeng, 2000, Beach water table fluctuations due to spring-neap tides: moving boundary effects. Adv Water Resour, 23, 817–824.http://dx.doi.org/10.1016/S0309-1708(00)00017-8

Moore, W. S., 1996, Large groundwater inputs to coastal waters revealed by 226Ra enrichment. Nature, 380, 612–614.http://dx.doi.org/10.1038/380612a0

Nielsen, P., 1990, Tidal dynamics of the water table in beaches. Water Resour. Res., 26, 2127–2134.

Parlange, J.–Y., F. Stagnitti, J. L. Starr and R. D. Braddock, 1984, Free-surface flow in porous media and periodic solution of the shallow-flow approximation. J. Hydrol., 70, 251-263. http://dx.doi.org/10.1016/0022-1694(84)90125-2

Philip, J. R., 1973, Periodic nonlinear diffusion: An integral relation and its physical consequences. Aust. J. Phys., 26, 513-519.http://dx.doi.org/10.1071/PH730513

Roberts, M. E., 2008,Groundwater response to tidal forcing. ANZIAM J. 50(CATA2008), C640- C653.

Song,Z. Y., L. Li, P. Nielsen and D. Lockington, 2006, Quantification of tidal watertable overheight in an unconfined coastal aquifer. J. Eng. Math., 56, 437-444.http://dx.doi.org/10.1007/s10665-006-9052-3

Song, Z. Y., L. Li, J. Kong and H. G. Zhang, 2007, A new analytical solution of tidal water table fluctuations in a coastal unconfined aquifer. J. Hydrol., 340,256-260.http://dx.doi.org/10.1016/j.jhydrol.2007.04.015

Teo, H. T., D. S. Jeng, B. R. Seymour, D. A. Barry and L. Li, 2003, A new analytical solution for water table fluctuations in coastal aquifers with sloping beaches. Adv Water Resour, 26, 1239–1247.http://dx.doi.org/10.1016/j.advwatres.2003.08.004

DOI: http://dx.doi.org/10.9753/icce.v32.currents.33