Stability Analysis for a Saline Boundary Layer Formed by Uniform Up ow Using Finite Elements

Up owing salty groundwater, evaporating completely at the ground surface, leads to the buildup of a saline boundary layer, usually with solid salt on the surface. The di usion layer below the surface, if stable, may grow to a nite thickness at equilibrium between the up owing salt and downward di usion. Because of the di erent densities of the uids (low fresh water density in the deeper underground and high salt water density at the boundary layer), gravitation plays a crucial role in the process and therefore it cannot be disregarded. For the instable case, at a critical Rayleigh number, perturbation of the system results in fresh-salt ngering of the boundary layer. The process described above is mathematically modelled using a scaled, coupled and nonlinear set of partial di erential equations for the incompressible uid including a convection-di usion equation and Darcy's law. In this report we rst give an overview of semi-analytical methods to analyse the stability of the boundary layer. Subsequently we focus on Finite Element (FEM) solutions of the governing equations to validate numerically the semi-analytical stability bounds. Furthermore, we analyse stability with respect to several kinds of perturbations.