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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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

The current theory for defining the occurrence of riparian lenses (i.e., buoyant, lenticular‐shaped fresh groundwater bodies overlying saline groundwater in riparian zones) is largely based on steady‐state analyses, which neglect the transient dynamics expected in real‐world settings. In this study, the transience of riparian lens movement is investigated for the first time, considering a fully penetrating, gaining river (i.e., the river receives groundwater influxes), and rapid variations in hydraulic boundary conditions. Controlled laboratory experiments and numerical modeling are used to determine the timescales associated with lens movements. Both numerical and experimental timescales show asymmetric behavior in the growth and decline of lenses, whereby growing lenses involve longer timescales than those of shrinking lenses. Inverse relationships between timescales and final hydraulic gradients are observed, such that higher final hydraulic gradients involved shorter timescales. Results also revealed a time lag in the movement of the lens tip (i.e., where the lens and water table intersect) relative to the lens toe (i.e., intersection of the lens with the riverbank). Riparian lenses have near‐identical timescales regardless of whether the river water or aquifer hydraulic head varies, and rather, timescales are more sensitive to the final hydraulic gradient. Application of typical parameter ranges for the River Murray (South Australia) floodplains reveals timescales of years to more than a decade to expand the riparian lens by tens of meters. Insights into riparian lenses transience attained from the current study build on the understanding of transience obtained for other mixed‐convective hydrogeological processes, such as seawater intrusion and retreat.

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Please cite this article as: Jazayeri Shoushtari, S.M.H., Cartwright, N., Perrochet, P., Nielsen, P., Influence of hysteresis on groundwater wave dynamics in an unconfined aquifer with a sloping boundary, Journal of Hydrology (2015), doi: http://dx.doi.org/10. 1016/j.jhydrol.2015.11.020 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. AbstractIn this paper, the influence of hysteresis on water table dynamics in an unconfined aquifer was examined using a numerical model to solve Richards unsaturated flow equation.The model was subject to simple harmonic forcing across a sloping boundary with a seepage face boundary condition.Time series from both hysteretic and non-hysteretic models were subject to harmonic analysis to extract the amplitude and