An analytical solution representing groundwater–surface water interaction

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.

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