A new analytical solution for water table fluctuations in coastal aquifers with sloping beaches
The Boussinesq equation appears as the zeroth-order term in the shallow water flow expansion of the non-linear equation describing the flow of fluid in an unconfined aquifer. One-dimensional models based on the Boussinesq equation have been used to analyse tide-induced water table fluctuations in coastal aquifers. Previous analytical solutions for a sloping beach are based on the perturbation parameter, epsilon(N) = alphaepsilon cot beta (in which beta is the beach slope, alpha is the amplitude parameter and epsilon is the shallow water parameter) and are limited to tan(-1) (alphaepsilon) much less than beta less than or equal to pi/2. In this paper, a new higher-order solution to the non- linear boundary value problem is derived. The results demonstrate the significant influence of the higher-order components and beach slope on the water table fluctuations.
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Teo, H. T., Jeng, D. S., Seymour, B. R., Barry, D. A., & Li, L. (2003). A new analytical solution for water table fluctuations in coastal aquifers with sloping beaches. Advances in Water Resources, 26(12), 1239–1247. https://doi.org/10.1016/j.advwatres.2003.08.004
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