Dynamics of shear layers at the interface of a highly porous medium and a pure fluid

In this paper, we report on shear flows in domains that contain a macroscopic interface between a highly porous medium and a pure fluid. Our study is based on the single-domain approach, according to which, the same set of governing equations is employed for both inside the porous medium and in the pure-fluid domain. In particular, we introduce a mathematical model for the flows of interest that is derived directly from a continuum theory for fluid-saturated granular materials. The resulting set of equations is a variation of the well-known unsteady Darcy-Brinkman model. First, we employ this model to perform a linear stability analysis of inviscid shear layers over a highly porous medium. Our analysis shows that such layers are unconditionally unstable. Next, we present results from numerical simulations of temporally evolving shear layers in both two and three dimensions. The simulations are performed via a recently designed algorithm that employs a predictor-corrector time-marching scheme and a projection method for the computation of the pressure field on a collocated grid. According to our numerical predictions, the onset of the Kelvin-Helmholtz instability leads to the formation of vortices that extend to both sides of the material interface, thus producing substantial recirculation inside the porous medium. These vortices eventually merge, leading to significant growth of the shear layer and, in three dimensional flows, transition to turbulence. The dynamics of the shear layers, including growth rate and self-similarity, is presented and analysed. Finally, the structure of these layers is described in detail and compared to the one of plain mixing layers.