This paper presents an analytical solution of linearized Boussinesq equation characterizing transient groundwater flow in a downward sloping unconfined aquifer of semiinfinite extent. The aquifer is in contact with a water body of constant water level at one end and receives localized vertical recharge at a constant rate from a linear recharge basin of finite width. In this idealization, the recharge basin can be located anywhere in the domain, thus its location is treated as an additional parameter. The flow equation is solved using Laplace transform to obtain transient expressions for aquifer piezometric head and flow rate at the interface. The effects of bed slope and the location of recharge basin on the phreatic surface are illustrated by taking a numerical example. The analytical results obtained for horizontal as well as sloping aquifers show that there is considerable increase in the mound height as the recharge basin is shifted away from the interface of aquifer and water body. Moreover, contrary...

This paper presents an analytical solution of the linearized Boussinesq equation characterizing the unsteady flow in an unconfined sloping aquifer that is in contact with a constant piezometric head at one end and a stream, whose level is rising at a constant rate, at the other end. Considering the idealized one-dimensional region as homogeneous, isotropic, incompressible, and an unconfined aquifer, the analytical expressions for the transient water table and the flow rate at both interfaces are obtained. The governing equations are solved by applying the Laplace transform technique and the results show a considerable change in aquifer’s water head profile and flow rate at the interfaces due to the presence of bed slope. The solution presented here is capable of handling the transient condition, as well as a very slow rise and a sudden rise in stream water for downward and upward sloping bedrocks after employing an asymptotic approach to corresponding scenarios.

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...