Interface and mixing zone between soil waters arising from upward and downward seepage - Part I: Homogeneous total density

•Modelling shallow water lenses with upward seepage and downward infiltration.•Analytical expressions of the sharp interface and its movement.•Approximate mixing zone midway between the drains.•Results of obtained expressions match with numerical model SUTRA. Thin water lenses floating on top of the main groundwater body are important for many natural and agricultural systems, owing to their different properties in terms of chemical composition or density compared to the surrounding groundwater. In settings with upward seeping groundwater, lenses may form that have thicknesses ranging from tens of centimeters to a few meters, making them prone to changing conditions in the short (seasonal) or long term (climate change). Knowing their thickness, shape, movement and mixing zone width may help in managing these lenses. In a series of two papers, we present a mathematical description of the flow of water and transport of solute in a 2D cross-section between two parallel outflow faces and compare a simplified model to a complete model as described by the numerical code SUTRA. In this first paper of the series, we consider situations with a homogeneous density distribution. In the simplified model we employ the sharp interface approximation to obtain an expression for the stream function, the interface between the two types of water and the corresponding maximum lens thickness in steady state in the domain considered. This steady state description is used for travel time analyses and forms the basis for the transient analyses. For a typical example of oscillatory (e.g. seasonal) fluctuations in boundary conditions, we obtain expressions of the movement of the interface midway between two outflow faces by separating the problem into two timescales using the interface motion equation. This analysis provides insight into the importance of parameters on the vulnerability of water lenses under changing conditions, and may easily be extended to situations with abrupt or gradual changes in boundary conditions reflecting changes in land use or climate, respectively. Finally, we derive an analytical approximation of the mixing zone midway between the drains for steady state solutions, stepping away from the sharp interface approach. For a variety of examples, we validate the obtained expressions of the simplified mathematical model against the numerical model code SUTRA, which solves the fluid and solute mass balances explicitly.