Transient Dupuit interface flow with partially penetrating features

A comprehensive potential is presented for Dupuit interface flow in coastal aquifers where both the fresh water and salt water are moving. The resulting potential flow problem may be solved, for incompressible confined aquifers, using analytic functions. The vertical velocity of the interface may then be computed analytically and the change of the position of the interface may be simulated by numerical integration through time, starting with a known (or estimated) initial position. The upconing of the interface below a partially penetrating ditch or well may be studied if Dupuit solutions for such features are available. A new Dupuit solution is derived for a ditch that penetrates the aquifer partially from above; a Dupuit solution for a partially penetrating well may be obtained following a similar derivation. The new Dupuit solution is combined with the interface solution to simulate the upconing of an initially horizontal interface below a series of partially penetrating ditches; the interface converges to the known steady state position.