Modeling instability development in layered systems

Abstract

This study investigates patterns of finger development and propagation in layered porous media. Fingers are created with interfacial perturbations, formed by adding a thin zone of regularly varying hydraulic conductivity along the layer. Simulation results agree qualitatively with those observed in two-dimensional laboratory experiments. In all cases, the formation of instabilities requires seeding of perturbations, even if the system is unstably stratified. A series of simulations show how the shapes of the instabilities differ according to where along the unstable interface the instabilities form and the layer in which they develop. Pathline analyses indicate how the patterns of flow in the domain can be exceedingly complex. Concentration distributions are influenced by movements of water between layers and the formation of a large convection cell in the lowermost layer. These numerical investigations reinforce inferences from the experimental studies that classical stability theory is less useful in determining whether instabilities will form and what their shape will be. Even with the relatively simple layering, patterns of flow and resulting concentrations are complex.