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.

This paper presents a new laboratory sand flume dataset on the propagation of groundwater waves in an unconfined sandy aquifer with a vertical boundary subject to simple harmonic forcing with a wide range of oscillation period from 10.7s to 909s. The data is unique in that it covers a much wider range of non-dimensional aquifer depths, nωd/K (where n is the porosity, ω is the angular frequency, d is the aquifer depth and K is the hydraulic conductivity) than has been previously investigated. Both the amplitude decay rate and rate of increase in phase lag of the water table waves are observed to monotonically increase with increasing oscillation frequency (increasing nωd/K). This is in contrast to existing theoretical dispersion relations which predict: (1) zero phase lag or standing wave behaviour and (2) an asymptotic decay rate as the frequency increases. Possible influences on the experimental data including sand packing, measurement location, finite amplitude wave effects, unsaturated zone truncation and multiple wave mode effects are unable to explain the discrepancy. The data was also compared against numerical solutions of Richards' equation with and without hysteresis and in both cases, the same qualitative behaviour as the analytic solutions described above is found. The discrepancy between data and predictions remains unexplained and highlights a knowledge gap that requires further 3 investigation. These findings relate directly to practical applications in the field of surface-groundwater interactions such as the influence of wave forcing of coastal aquifers on contaminant transport, sediment mobility and salt-water intrusion all of which are influenced by the dispersion of the groundwater wave.

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