A new analytical solution for water table fluctuations in coastal aquifers with sloping beaches |
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| Authors: | H. T. Teo D. S. Jeng B. R. Seymour D. A. Barry L. Li |
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| Affiliation: | 1. School of Engineering, Griffith University Gold Coast Campus, Qld 9726, Australia;2. Department of Mathematics, The University of British Columbia Vancouver, Canada V6T 1Z2;3. Contaminated Land Assessment and Remediation Research Centre, Institute for Infrastructure and Environment, School of Engineering and Electronics, The University of Edinburgh, Edinburgh EH9 3JN, UK;4. School of Engineering, The University of Queensland, Qld 4072, Australia;5. Centre for Eco-Environmental Modelling, Hohai University, Nanjing 210098, PR China;1. Department of Geology and Geophysics, Texas A&M University, College Station, TX 77843-3115, USA;2. Guangdong Provincial Key Laboratory of Soil and Groundwater Pollution Control, School of Environmental Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China;3. School of Mathematics and Physics, China University of Geosciences, 388 Lumo Road, Wuhan 430074, China;1. University of Southern Queensland, Institute for Advanced Engineering and Space Sciences, Toowoomba, QLD 4350, Australia;2. University of Southern Queensland, School of Mechanical and Electrical Engineering, Faculty of Health, Engineering and Sciences, Toowoomba, QLD 4350, Australia;3. CSIRO Agriculture and Food, Canberra, ACT 2601, Australia;4. University of Southern Queensland, Centre for Agricultural Engineering, Toowoomba, QLD 4350, Australia;5. Federal University of Rio de Janeiro, Department of Nuclear Engineering, Rio de Janeiro, Brazil;6. São Paulo State University, Center for Environmental Studies, CEA, Rio Claro, Brazil;1. Deltares, Department of Soil and Groundwater, P.O. Box 85467, 3508 AL Utrecht, The Netherlands;2. Wageningen University, Environmental Sciences Group, Soil Physics and Land Management, P.O. Box 47, 6700 AA Wageningen, The Netherlands;3. VU University Amsterdam, Faculty of Earth and Life Sciences, Hydrology and Geo-Environmental Sciences, Boelelaan 1085, 1081 HV Amsterdam, The Netherlands;4. University of Ghent, Department of Geology and Soil Science, Krijgslaan 281 S8, B-9000 Ghent, Belgium |
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| Abstract: | 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, N=αcotβ (in which β is the beach slope, α is the amplitude parameter and is the shallow water parameter) and are limited to tan−1(α)βπ/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. The relative difference between the linear solution and the present solution increases as and α increase, and reaches 7% of the linear solution. |
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| Keywords: | Groundwater Hydraulic conductivity Moving boundary Coastal aquifer |
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