Thermal convection is a phenomenon seen in almost all facets of life, ranging from planetary convection to ocean currents and convection inside the Earth. The physics of thermal convection complicates when a porous wall layer is present. Flow over urban canopies, forest canopies or flow in underground aquifers are classic examples where thermal convection occurs in the presence of turbulent flow over a medium that may be described as a porous wall layer. The present work focuses on simulating pressure-driven turbulent flow over a simplified, ordered porous medium consisting of a regular array of cubes. The work further couples it with natural convection arising due to unstable stratification, to provide insight into its momentum and heat transfer characteristics. Direct numerical simulations (DNS) have been performed with a finite-difference Navier-Stokes solver to validate the model for buoyancy-driven convection and the classical Rayleigh-B´enard convection. Further, we extended the solver with a volume penalization Immersed Boundary Method (IBM) to model the ordered porous medium, which was validated against reference data. The bulk Reynolds in the overlying free channel region is fixed at 5500, the Prandtl number at 0.1, with an adiabatic boundary condition on the surface of the cubes. The bulk Richardson number, to cover different flow scenarios, from pure shear to purely buoyancy-driven flows, is also varied. The flow statistics show three distinct regimes spatially, (1) the porous region, (2) the turbulent channel and (3)the interface regime, where heat transfer timescales vary drastically between the porous region and the turbulent flow region. Looking at the regime transition from the perspective of changing Rib, the change starts at about bulk Richardson number Rib ≈ 0.1, with the flow switching from mostly buoyancy dominated to shear-dominated convection. The possible regimes as a function of the governing parameters are described, with three regimes formed using critical Rayleigh number limits for convection in free media and in porous media. The qualitative analysis of the thermal structures formed reveals, indeed, that the theorized critical limits are indeed seen through simulations. Lastly, length and velocity scalings are also suggested separately for shear-driven and buoyancy-driven regimes for different regions of the flow domain.