Analytic solutions for fresh groundwater lenses floating on saline water under desert dunes: The Kunin-Van Der Veer legacy revisited

A fully-saturated lens of steady fresh groundwater floating in a homogeneous and isotropic desert sandy aquifer is analytically studied based on a hydrological model by Kunin and interface solution by Van Der Veer. A static saline groundwater is beneath the lens. A phreatic surface of moving fresh water inside the lens is partially recharged (either naturally or by managed aquifer recharge) from the vadose zone and partially exfiltrates to it. A spatially focused recharge and intensive evapotranspiration preserve a steady downward-upward topology of fresh water motion. In terms of the 1-D Dupuit-Forchheimer approximation in a horizontal in-lens saturated flow a boundary value problem (BVP) for an ODE for the Strack potential is solved. The shape of the water table and, based on the Ghijben-Herzberg assumption, the interface are found. The total volume of the positive-pore pressure water flowing within the lens is evaluated. Constant infiltration and evaporation rates as well as evaporation linearly decreasing with depth of the water table (counted from the ground surface) are considered. The case of 2-D flow is tackled by the Toth model. A triangular analytic element approximates a half of the flow domain and consists of an isobaric side and two no-flow sides. Conformal mapping of this triangle onto a reference plane and solution of the Dirichlet BVP in a half-plane deliver the distribution of infiltration-exfiltration intensity along the water table, total flow rate and locus of the hinge point. A mathematically more cumbersome approximation of the flow domain assumes the water table to be a tilted straight line but the interface to be found as a free boundary. Solution of the corresponding BVP uses a curvilinear triangle in the hodograph plane.