UC Santa Barbara

The equation of groundwater flow in marine island aquifers in which there is time-independent, spatially-variable recharge and pumping is solved in closed form for rectangular, circular, and elliptical island geometries. The solution of the groundwater flow equation is expressed in terms of the elevation of the phreatic surface within the flow domain. The depth of the seawater-freshwater interface below mean sea level follows from the Dupuit-Ghyben-Herzberg relation. The method of solution presented in this work relies on expanding the hydraulic head and forcing function (recharge and groundwater extraction) as Fourier series that transforms the two-dimensional Poisson-type flow equations into second-order ordinary differential equations solvable using classical theory. The important case of constant recharge (without groundwater extraction) leads to solutions in which the hydraulic head is expressible as the product of a flow factor equal to the squared root of the ratio of recharge over hydraulic conductivity times a geometric factor involving island shape parameters and flow boundary conditions. Estimability conditions for the hydraulic conductivity are derived for the cases of constant recharge and spatially variable recharge with pumping. © International Association for Mathematical Geology 2008.