ABSTRACT

We explore the problem of a slumping gravity current in the presence of a variable coefficient porous medium. We identify similarity variables and solutions for the constant coefficient case. Using methods of homogenized averaging generalize to this nonlinear problem involving a moving boundary condition we make a connection to these similarity scalings in the case of variable coefficient layered media. By simplifying to a thin gravity current, retaining horizontal variations of the porous media, we derive a variable coefficient scalar nonlinear partial differential equation governing the moving interfaces. Through a combination of explicit homogenization retaining leading order plus first correction and comparison between full simulation of this simplified one dimensional problem, we document the success of the homogenization approach in this nonlinear problem. These corrections exhibit a spatial imprint of the properties of the porous medium.