Withdrawal from the lens of freshwater in a tropical island: the two interface case

Fresh water held in the soil beneath a tropical island is one source of drinking water for the island population. If recharge through rainfall is insufficient, this resource may drain away. This work considers the circumstances under which artificial recharge will maintain the lens of freshwater. A Green function approach is used to derive an integral equation that is solved numerically for the case in which there exist two interfaces one between salt and freshwater and one between freshwater and air. There appear to be bounds on the flow rates that produce steady interface shapes, but the height of the seepage faces is affected much more by the density ratios than the flow rates. Several different scenarios of withdrawal and influx are considered with a goal of determining some optimal management strategies.