An analytical solution representing groundwater–surface water interaction

Abstract

[1] An analytical solution is developed and used to examine groundwater-surface water interaction at streams; we consider two-dimensional, steady groundwater flow in the vertical plane. The aquifer is idealized as an infinite strip, and the streambed is modeled as a horizontal equipotential. Segments of constant recharge are applied along the boundaries of the infinite strip. Explicit analytical solutions for the complex potential and complex specific discharge are developed using conformal mapping, the method of images, and boundary integral techniques. The expressions for the complex specific discharge may be used to identify and quantify the numerous groundwater flow regimes first identified by Nield et al. [1994]. We demonstrate this by evaluating the conditions required for transition from a flow-through regime to a flow-through regime with a zone of reverse flow.

Impact of rehabilitation of Assiut barrage, Nile River, on groundwater rise in urban areas

“…Dawoud (1997) modified a two-dimensional multilayer groundwater flow model for simulating a stream/aquifer interaction. Numerous researchers including Morel-Seytoux et al (1985), Peralta et al (1990), Ahlfeld and Minihane (2002), and Anderson (2003) treated the interaction between the stream and aquifer as a time dependant third type boundary condition (Cauchy Boundary Condition). The same mathematical approach used to describe stream/aquifer interaction can be used to describe interflows between a reservoir and an underlying aquifer.…”

The Turning Factor in the Estimation of Stream‐Aquifer Seepage

“…(For a recent overall review of the literature, the reader may refer to this publication, which contains 33 references. The reader may also consult Anderson [2003].) The case studied here is germane to the situation of a losing stream in hydraulic connection with the aquifer.…”

Three-dimensional groundwater flow to a shallow pond: An explicit solution

“…Kacimov (2000) derived a simple rigorous solution to a seepage problem for a hemispherical lake placed in an incident groundwater flow. A natural question that ensued from the results by Kacimov (2000) for an axisymmetric regime, by Strack (1989) for a 2-D flow near a fully penetrating cylindrical lake, and by Anderson (2003) for a shallow canal placed perpendicularly to the incident flow is: is there an explicit closed-form solution for a genuinely 3-D nonaxisymmetric case? In this paper we provide such a solution for a shallow circular water body that will be called a pond.…”