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

Steady groundwater flow near a shallow disk-shaped pond, the bottom of which is in direct hydraulic contact with a confined homogeneous aquifer, is studied analytically by the Fabrikant method of L-operators. For the case of a unidirectional flow at infinity a rigorous and explicit expression for the hydraulic head and specific discharge components are obtained. Depending on the ambient specific discharge, aquifer conductivity, pond radius, and the pond bottom head three regimes (gaining, losing and flow-through) of pond water-groundwater interaction are explicitly demarcated. The hinge line on the pond bottom for the flow-through regime is shown to be a straight line. The only stagnation point in the gaining regime is found from a simple nonlinear equation. Closed-form expressions for the total pond seepage rate and inflow-, outflow-rates are presented. Streamlines and isochrones of groundwater travel time are found by a particle-tracking method. The capture and release zones of the pond are outlined.