Previous studies of freshwater lenses in saline aquifers adjoining gaining rivers ("riparian lenses") have so far considered only rivers that fully penetrate the aquifer, whereas in most cases, rivers are only partially penetrating. This paper presents a new methodology for obtaining the saltwater discharge and the shape of a steady-state, non-dispersive riparian lens, where the river is partially penetrating, combining two previous analytical solutions. The resulting analytical solution is compared to numerical modeling results to assess assumptions and the methodology adopted to approximate the "turning effect," which is the change in groundwater flow direction (horizontal to vertical) near the partially penetrating river. Model parameters were taken from previous studies, representing simplified conditions in the River Murray floodplains (Australia). Consistency between analytical and numerical results and field observations highlights the capability of the proposed analytical solution to predict the riparian lens geometry and saltwater discharge into partially penetrating rivers. Sensitivity analysis indicates that larger riparian lenses are produced adjacent to the deeper and wider rivers, as expected. The change in width or depth of the river has more influence on the saltwater discharge and the horizontal extent of the riparian lens (and less effect on the vertical extent of the lens adjacent to the river) for shallower and narrower rivers. This research highlights the utility of the new method and demonstrates that the assumption of a fully penetrating river likely leads to significant overestimation of the saltwater discharge to the river and the riparian lens horizontal extent and vertical depth.

Freshwater lenses within riparian zones of some arid and semiarid settings assist in maintaining the health of riparian ecosystems. We propose an approach for expanding freshwater lenses in saline aquifers adjacent to gaining rivers through the addition of a vertical barrier of low‐hydraulic‐conductivity (low‐K) parallel to the river bank. Sharp‐interface analytical solutions for the lens shape and water table distribution are developed to examine the effectiveness of the proposed method and are verified using sand tank experiments and numerical simulations. The sensitivity analysis is used to apply the method to parameters typical of the Lower River Murray (South Australia) and its floodplain aquifers. The results show that the barrier can create significant freshwater lenses in head‐controlled systems, whereas the barrier may lead to lens shrinkage in flux‐controlled systems due to saline water table rise. That is, the effectiveness of the barrier is highly dependent on the inland boundary condition. The analytical solution presented herein can be used to efficiently predict the riparian freshwater lens extent in response to engineered barriers, adding to existing techniques for studying and modifying riparian freshwater lenses.

Freshwater lenses have been observed within riparian aquifers where freshwater rivers traverse and connect to saline groundwater (e.g., Cendón et al., 2010;Laattoe et al., 2017). Such settings are encountered in arid and semi-arid regions where saline groundwater often occurs because of significant evapo-concentration effects (Alaghmand et al., 2013;Bauer et al., 2006). The fresh groundwater found in riparian zones (i.e., buoyant, lenticular-shaped freshwater bodies adjacent to rivers; "riparian lenses" hereafter) play an important role in sustaining fragile riparian and floodplain ecosystems (e.g., the Chowilla floodplain, South Australia; Holland et al., 2009) in arid and semi-arid regions, particularly during low-flow periods (e.g., Holland