Salt-water up-coning during extraction of fresh water from a tropical island

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.