Effects of Bed Slope on Water Head and Flow Rate at the Interfaces between the Stream and Groundwater: Analytical Study

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.