Abstract
The lens of freshwater beneath a tropical island is vital for supplying water to the island population. We consider the circumstances under which artificial recharge through a single inlet point will maintain the lens if no natural recharge occurs. A Greens function approach derives an integral equation that is solved numerically for the case in which two interfaces exist---one between salt and freshwater and one between freshwater and air. There appear to be upper and lower bounds on the flow rates that produce steady interface shapes. The height of the seepage faces is dominated by the density ratios. References L. K. Forbes, G. C. Hocking and S. Wotherspoon, 2004, Salt-water up-coning during extraction of fresh water from a tropical island, J. Eng. Math , 48 , 2004, 69--91. doi:10.1023/B:ENGI.0000009517.28682.6f G. C. Hocking and L. K. Forbes, The lens of freshwater in a tropical island - 2d withdrawal, Comp. and Fluids , 33 , 2004, 19--30. doi:10.1016/S0045-7930(03)00035-5 G. C. Hocking and H. Zhang, A note on withdrawal from a two-layer fluid through a line sink in a porous medium, ANZIAM J. , 50 , 2008, 101--110. doi:10.1017/S144618110800028X C. D. Langevin, M. T. Stewart and C. M. Beaudoin, Effects of sea water canals on fresh water resources: an example from Big Pine Key, Florida, Ground Water , 36 , 1998, 503--513. doi:10.1111/j.1745-6584.1998.tb02822.x S. K. Lucas, J. R. Blake and A. Kucera, A boundary-integral method applied to water coning in oil reservoirs, J. Austral. Math. Soc. Ser. B , 32 , 1991, 261--283. doi:10.1017/S0334270000006858 M. Muskat and R. B. Wyckoff, An approximate theory of water coning in oil production, Trans. AIME , 114 , 1935, 144--163. P. Y. Polubarinova-Kochina, Unsteady seepage with an interface (in Russian), Moscow: Dokl. Nauk, S. S. S. R. , 1949, 173--176 C. Ruppel, G. Schultz and S. Kruse, Anomalous fresh water lens morphology on a strip barrier island, Ground Water , 38 , 2000, 872--881. doi:10.1111/j.1745-6584.2000.tb00686.x H. Zhang and G. C. Hocking, Withdrawal of layered fluid through a line sink in a porous medium, J. Austral. Math. Soc. Ser. B , 38 , 1996, 240--254. doi:10.1017/S0334270000000631
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