209 Variable-density flow in porous media

Steady-state distributions of water potential and salt concentration in coastal aquifers are typically modelled by the Henry problem, which consists of a fully coupled system of flow and transport equations. Coupling arises from the dependence of water density on salt concentration. The physical behaviour of the system is fully described by two dimensionless groups: (i) the coupling parameter α, which encapsulates the relative importance of buoyancy and viscous forces, and (ii) the Péclet number Pe, which quantifies the relative importance of purely convective and dispersive transport mechanisms. We provide a systematic analytical analysis of the Henry problem for a full range of the Péclet number. For moderate Pe, analytical solutions are obtained through perturbation expansions in α. This allows us to elucidate the onset of density-driven vertical flux components and the dependence of the local hydraulic head gradients on the coupling parameter. The perturbation solution identifies the regions where salt concentration is most pronounced and relates their spatial extent to the development of a convection cell. Next, we compare our solution to a solution of the pseudo-coupled model, wherein flow and transport are coupled only via th