Rajeev K. Bansal

In this paper, new analytical solutions are presented to quantify interaction of water between a sloping aquifer and stream of varying heads in presence of a thin vertical sedimentary layer. The initial hydrogeological setting consist of an unconfined sloping aquifer of semi-infinite extent, a fully penetrating stream of varying water level, and a vertical layer of streambank deposits that acts as an interface between stream and aquifer. Unsteady groundwater flow is characterized by a nonlinear Boussinesq equation subject to Robin boundary condition (also referred to as third kind and Cauchy boundary condition). Unlike existing results, which focus only on step changes in stream stage, the current study accounts for gradual rise and decline in stream level. A closed-form analytical solution for water head distribution, discharge rate, and net volumetric exchange of water between stream and aquifer are developed from the solution of a linearized advection-diffusion equation. Performance of the anal...

This paper analyzes the groundwater flow system in an unconfined downward-sloping aquifer of semi-infinite extent in response to localized transient recharge. The aquifer is in contact with a water body of constant water level at one end and receives localized transient recharge from a recharge basin of finite width. The mathematical model is based on the Boussinesq equation with Dupuit-Forchheimer assumption, in which the spatial coordinate of the recharge basin is treated as an additional parameter. Analytical solutions of the linearized Boussinesq equation are obtained using the Laplace transform technique by dividing the aquifer in a three-zone system containing both Dirichlet and Neumann boundary conditions at the hypothetical interfaces. Upward- and zero-sloping cases are deduced from the main results by appropriately adjusting the slope parameter. To assess the validity and efficiency of the linearization method, the nonlinear Boussinesq equation is also solved using a fully explicit predictor-corrector numerical scheme. A numerical example is used for illustrating the effects of various parameters such as aquifer’s bed slope, spatial coordinate of the recharge basin, and recharge rate on the dynamic profiles of phreatic surface.