An analytical solution for groundwater flow incorporating the effect of water bodies with sloping surfaces

Determination of hyporheic flow between surface water and groundwater is crucial to clarify the coupled water systems' hydrological and ecological behaviour. Therefore, this study focuses on groundwater systems interacting with water bodies with sloping surfaces. A sloping stream is defined as an aquifer's boundary condition. A recharge/discharge term is incorporated into the groundwater flow equation to represent the flux between groundwater and a water body with a sloping surface. An analytical solution of the groundwater flow equation is derived for a homogeneous and isotropic aquifer of a steady-state case. Additionally, a numerical algorithm is written for comparison purposes. The effect of water surface slope on the groundwater head distribution in the horizontal plane and the flux between surface water and groundwater is investigated. The results show that the analytical solution represents the hydrodynamics of the stream-water body-aquifer system well, and the water surface slope is dominant on surface water-groundwater interactions.