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

•Modelling shallow water lenses with upward seepage and downward infiltration.•Approximations of the interface position under heterogeneous density distribution.•Heterogeneous density distributions result in shallower water lenses.•Oscillations in interface position are hardly affected by heterogeneous density distribution. Freshwater lenses in otherwise saline environments contain an important source of fresh water for natural vegetation and agricultural crops. Such lenses are regularly found in areas where both upward seeping saline groundwater and downward infiltrating fresh recharge water occur simultaneously during part of the year, resulting in shallow freshwater lenses which are highly susceptible to changes in recharge or seepage. In a series of two papers, we consider the water – and solute transport in a 2D cross-section between two parallel outflow faces. In this second part of the series, we build upon expressions presented in the first part to consider a situation where the density of seepage water exceeds that of recharge water, as typical for many deltaic areas around the world. Analytical expressions and approximations are given to obtain the steady state position of the interface between the two types of water using a sharp interface approximation, with a focus on the position midway between two outflow faces. Results show that the effect of a heterogeneous density distribution is limited when the seepage flux exceeds the density difference induced flux, but increases rapidly for ratios of the seepage flux over the density flux falling below 1. The heterogeneous density distribution then results in a decrease in freshwater lens thickness and, correspondingly, a decrease in fresh water availability. We also consider time-variant, oscillatory boundary conditions, and show that for heterogeneous density distributions the interface approaches its equilibrium position faster than for a corresponding situation with a homogeneous density distribution, indicating a higher vulnerability for changing boundary conditions. We also demonstrate that heterogeneous density distributions have limited effect on the amplitude of the interface oscillations. Analytical results obtained with the simplified model are validated using the numerical code SUTRA, which solves the full model for a numerical grid.