Abstract
Rainwater can collect in a lens-shaped region within the rock of a tropical island, and may be separated from the underlying salt water by a sharp interface. This paper presents a nonlinear theory for determining the shape of this interface. The island is assumed to be saturated with rain, and provision is made for the outflow of rain-water through the sides of the island. The effect of a bore well on the shape of the interface is investigated, and the problem is solved using a spectral method. An integral-equation method is also presented for the case when the island has infinite width.
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Forbes, L.K., Hocking, G.C. & Wotherspoon, S. Salt-water up-coning during extraction of fresh water from a tropical island. Journal of Engineering Mathematics 48, 69–91 (2004). https://doi.org/10.1023/B:ENGI.0000009517.28682.6f
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DOI: https://doi.org/10.1023/B:ENGI.0000009517.28682.6f