Buoyancy-driven convection in a horizontal fluid layer extending over a porous substrate

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Abstract
In this study a series of numerical simulations is reported that aims to document the phenomenon of buoyancy‐driven flow instability in a fluid layer extending over a porous substrate. The numerical simulations focus primarily on the parametric domain in which the flow in the system is well established, i.e., the value of the Rayleigh number is larger than critical. A general flow model is used to describe the flow inside the porous bed. This flow model accounts for friction caused by macroscopic shear [Brinkman extension of the Darcy model; Appl. Sci. Res. Sect. A 1, 27 (1947)], as well as for the phenomenon of flow inertia [Forchheimer’s extension of the Darcy model; Dtsch. Ingenieure 4 5, 1782 (1901)]. Several important characteristics of the flow and temperature fields inside the composite layer (porous/fluid) are reported and the dependence of these characteristics on the problem dimensionless groups is documented.