On the Maas problem of seawater intrusion combated by infiltration

The problem of Maas [Maas, K. 2007. Influence of climate change on a Ghijben–Herzberg lens. J. Hydrol. 347, 223–228] for infiltration inflow into a porous flat-roofed fresh water lens floating on the interface of an ascending Darcian saline water flow is shown to be in exact match with the Polubarinova-Kochina [Polubarinova-Kochina, P.Ya., 1977. Theory of Ground Water Movement. Nauka, Moscow (in Russian)] problem for flow in a lens capped by a cambered phreatic surface with a uniform accretion. The Maas complex potential in the domain of a heavy saline water seeping beneath the lens corresponds to one of an ideal fluid flow past an elliptical cylinder that makes possible conversion of this potential into ascending–descending seepage flows with floating (but stagnant) DNAPL-LNAPL volumes. Similar matching is possible for the velocity potential of an axisymmetric flow past an ellipsoid and hydrostatic pressure of a stagnant NAPL body stored in a semi-ellipsoidal pond.