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Water-table response to tidal forcing at sloping beaches

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Abstract

The groundwater response to tidal forcing is described by Laplace’s equation for the hydraulic head subject to appropriate boundary conditions. A previous solution to this problem based on long-wave and shallow-aquifer approximations is extended to higher-order and a general solution scheme, automated in Mathematica, is described. The solution can, in principle, be extended to arbitrary order, but is restricted to a detailed study of the properties of the solution when truncated to sixth-order. These results show that the mean water table height increases throughout the aquifer to a steady inland height elevated above mean sea level. The phase shift of the fluctuations and the asymmetry of the pore drainage process are investigated using Fourier analysis.

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of Western Australia, Crawley, WA, 6009, Australia

    Melanie E. Roberts, N. Fowkes & Andrew P. Bassom

  2. CSIRO Land and Water, Private Bag No. 5, Wembley, WA, 6913, Australia

    M. G. Trefry

  3. School of Earth and Environment, University of Western Australia, Crawley, WA, 6009, Australia

    M. G. Trefry

  4. School of Physics, University of Western Australia, Crawley, WA, 6009, Australia

    P. C. Abbott

Authors
  1. Melanie E. Roberts
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  2. M. G. Trefry
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  3. N. Fowkes
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  4. Andrew P. Bassom
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  5. P. C. Abbott
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Correspondence to Melanie E. Roberts.

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Roberts, M.E., Trefry, M.G., Fowkes, N. et al. Water-table response to tidal forcing at sloping beaches. J Eng Math 69, 291–311 (2011). https://doi.org/10.1007/s10665-010-9407-7

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  • DOI: https://doi.org/10.1007/s10665-010-9407-7

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