Inclined porous medium convection at large Rayleigh number

High-Rayleigh-number (Ra) convection in an inclined two-dimensional porous layer is investigated using direct numerical simulations (DNS) and stability and variational upper-bound analyses. When the inclination angle phi of the layer satisfies 0 degrees < phi less than or similar to 25 degrees, DNS confirm that the flow exhibits a three-region wall-normal asymptotic structure in accord with the strictly horizontal (phi = 0 degrees) case, except that as phi is increased the time-mean spacing between neighbouring interior plumes also increases substantially. Both DNS and upper-bound analysis indicate that the heat transport enhancement factor (i.e. the Nusselt number) Nu similar to CRa with a phi-dependent prefactor C. When phi > phi(t), however, where 30 degrees < phi(t) < 32 degrees independently of Ra, the columnar flow structure is completely broken down: the flow transitions to a large-scale travelling-wave convective roll state, and the heat transport is significantly reduced. To better understand the physics of inclined porous medium convection at large Ra and modest inclination angles, a spatial Floquet analysis is performed, yielding predictions of the linear stability of numerically computed, fully nonlinear steady convective states. The results show that there exist two types of instability when phi not equal 0 degrees : a bulk-mode instability and a wall-mode instability, consistent with previous findings for phi = 0 degrees (Wen et al., J. Fluid Mech., vol. 772, 2015, pp. 197-224). The background flow induced by the inclination of the layer intensifies the bulk-mode instability during its subsequent nonlinear evolution, thereby favouring increased spacing between the interior plumes relative to that observed in convection in a horizontal porous layer.