Derivation of Seawater Intrusion Models by Formal Asymptotics

In this paper, we consider the flow of fresh- and saltwater in a saturated porous medium in order to describe the process of seawater intrusion. Starting from a formulation with constant densities of fresh- and saltwater, whose velocities are proportional to the gradient of pressure (Darcy's law), we consider the formal asymptotic limit as the aspect ratio between the thickness and the horizontal length of the porous medium tends to zero. In the limit of the regime defined by the Dupuit--Forchheimer condition, we identify reduced models of Boussinesq type in the cases of both unconfined and confined aquifers.