Modeling the evolution of three-layered Stokes flow and some geophysical applications

Abstract

Analytical investigation and numerical modeling have been fulfilled to study the evolution of Stokes flow in a computational domain that consists of thick viscous layer overlaid by a thin multi-layered viscous sheet. We obtain an analytical solution and explore the short- and long-time evolution of the velocity field and layer boundaries. Linear analysis of small perturbations reveals the evolution of the flow to be multistage. It consists of several stages with typical time scales. During the evolution the inversion of layer boundary relief and transformation of the velocity field from one-layered to three-layered structure happen. These time scales are evaluated with respect to geometrical and physical parameters of layers. We fulfill numerical modeling of the evolution of the velocity field and layer boundaries. For this purpose we apply the two-dimensional coupled model that consists of the Stokes equations describing the flow in the layer and the Reynolds equations describing the flow in the sheet. We take into account the layer structure of the sheet and surface processes of erosion and sedimentation as well. The model includes an additional asymptotic boundary condition that couples different-type hydrodynamic equations without any iterative improvements. This condition reduces significantly computational costs in comparison with the available coupled models. Numerical calculations for large perturbations of layer boundaries validate the results of analytical study. Some possible applications in tectonics and geophysics of these model results are outlined. They can be applied to investigate lithosphere thinning beneath large-scale tectonic depressions.