Surface water‐groundwater interaction near shallow circular lakes: Flow geometry in three dimensions

Abstract

Abstract. Steady flow regimes for three-dimensional lake-aquifer systems are studied via idealized mathematical models that are extensions of earlier simplified vertical section models of interaction between shallow lakes and underlying aquifers. The present models apply to a shallow circular lake at the surface of a rectangular aquifer of finite depth, yielding a truly three-dimensional representation of the resulting flow system. Flux boundary conditions are applied at the ends of the aquifer, with net vertical recharge or evapotranspiration at the water table. The lake is defined by a region with constant head. By determining and visualizing solutions to the discretized saturated flow equations, a range of possible flow regimes is identified, and their topological properties are studied. Tools for analyzing flow regimes are described, including a method for locating and mapping three-dimensional dividing surfaces within steady flow fields. Results show strong similarities between two-and three-dimensional systems, including a large number of flowthrough, recharge, and discharge regimes and reverse flow cells. Flow lines calculated on a vertical plane through the middle of a lake resemble but are not identical to twodimensional streamlines for a range of aquifer flow and recharge conditions. Estimates of the widths and depths of capture and release zones for various lake-aquifer geometries are asymptotic to earlier results for two-dimensional systems. Numerical predictions are compared with analytical results for certain limiting flow regimes.

Modeling the influence of land use on groundwater chloride loading to lakes

“…Lakes relatively long in the direction of groundwater flow relative to the aquifer depth are likely to intercept much of the groundwater flow (Hunt et al 2003). Townley and Trefry (2000) showed that a circular lake in an isotropic aquifer intercepts >90% of the flow when the lake diameter-to-aquifer thickness is >4. The ratio of lake length to aquifer thickness below the study lakes ranged from 6 to 40.…”

Combined use of frequency-domain electromagnetic and electrical resistivity surveys to delineate near-lake groundwater flow in the semi-arid Nebraska Sand Hills, USA

“…1, Q in is the inflow rate of fresh groundwater with concentration C in and Q out is the outflow rate with elevated concentration C out . Lake water of elevated salinity discharges into a groundwater system and moves downgradient with the ambient flow (Townley and Trefry 2000;Zlotnik et al 2009), interacting with it to produce a saline plume. This approach was tested in the Nebraska Sand Hills, Nebraska, USA.…”

“…Fresher, flow-through lakes are located above the dune dam where the hydraulic gradient is steep, whereas saline, gaining lakes occur far from the discharge point of a buried paleovalley, identified by Loope et al (1995) from core logs and radiocarbon dating, along which the hydraulic gradient is gentle. Aside from regional climate, other factors that control lake salinity include the topographic and hydrological position of the lakes within the regional groundwater system (Townley and Trefry 2000;Zlotnik et al 2009) and eolian transport of salt ).…”

An analytical solution representing groundwater–surface water interaction

“…The numerous regimes are identified by the presence and location of stagnation points in the flow field. More recently, Townley and Trefry [2000] used a similar approach to investigate the interactions of shallow circular lakes in confined aquifers; they develop numerical solutions for three-dimensional flow in a simplified problem domain. Their results show strong similarities between flow regimes in two-and three-dimensional systems.…”