Inertial Density Currents over Porous Media Limited by Different Lower Boundary Conditions

Abstract

We study the evolution of two-dimensional high-Reynolds-number density currents propagating over horizontal porous substrates initially saturated with a lighter fluid when an impermeable surface under the bed is used and a Darcy flow through the medium takes place. Laboratory experiments were performed varying the initial characteristic parameters such as the volume released, the height-to-width ratio of the dense fluid, the relative density difference between the current and ambient fluids, and the bed depth. The dynamic changes of the gravity-driven flow and the influence of the thickness of the porous substrate are described by means of an empirical analysis that considers two lower boundary conditions of the bed, that is, when it is bounded from below by an impermeable or a permeable layer. Thus, the new experimental results are integrated to previous findings in a unified theoretical treatment. In the present case, the dense fluid penetrates into the porous layer pushing the lighter one through the upper boundary located ahead of the current, as shown by the vorticity distribution, and modifying the interaction between the flows over and inside the bed. This flow in the neighborhood of the front, although important, is smaller than the one that would pass through the lower boundary if this were permeable.