Two-Dimensional Numerical Solution of Steady Withdrawal From the Lens of Freshwater in a Tropical Island

The work presented here is a study of the steady withdrawal of water from the lens of freshwater situated above the ocean’s salt water and within the island. It is the aim of this paper to investigate the process of withdrawal from the lens of freshwater with a view to establishing the critical flow values for withdrawal and the effects of sink location and density differences on these values, and also to determine the effects of relative density differences. Steady solutions are found for the shape of the interface between salt and freshwater beneath a tropical island. A Green_s function approach is used and proves to be much more robust than spectral methods. Computations of the surface shape during withdrawal through a line sink are described and the maximum pumping rate before critical breakthrough of the salt water is found for a range of different sink locations. The effects of density ratio, withdrawal depth and horizontal location are also calculated and found to be significant. Decreasing the density ratio between the layers, or increasing withdrawal height is shown to make a significant difference to the critical flow rate. Further, it is shown that for realistic densities, the island width can be a factor for quite substantial widths, whereas for higher, unrealistic density differences an increase in width quickly becomes irrelevant to the interface shape.