Time dependence of groundwater pumping from a well near a river

The time-dependent flow of groundwater through an aquifer, generated from rest by pumping from a well close to a river, is calculated without making Dupuit's approximation. The governing equations reduce to the diffusion equation for the pressure head with mixed boundary conditions at the surface of the aquifer and at the base of the river. Using transform techniques, the problem is reduced to an infinite set of linear equations. The steady-state solution provides a guide to the numerical solution of the time-dependent problem. Results are presented for the flux from the river into the aquifer as well as for the flux from the aquifer into the river and out again. Explicit expressions for these fluxes are obtained in the case of rivers that are narrow compared with the aquifer depth. The steady-state flux is then much smaller than the transient flux. Results are significantly different from those obtained using the Dupuit approximation.