Kelvin-Helmhotz Instability for Parallel Flow in Porous Media: A Linear Theory

Two fluid layers in fully-saturated porous media are considered. The lighter fluid is above the heavier one so that in the absence of motion the arrangement is stable and the interface is flat. It is shown that when the fluids are moving parallel to each other at different velocities, the interface may become unstable (the Kelvin-Helmholtz instability). The corresponding conditions for marginal stability are derived for Darcian and non-Darcian flows. In both cases, the velocities should exceed some critical values in order for the instability to manifest itself. In the case of Darcy's flow, however, an additional condition, involving the fluids' viscosity and density ratios, is required.