On Moderate-Rayleigh-Number Convection in an Inclined Porous Layer

We investigate the flow structure and dynamics of moderate-Rayleigh-number (Ra) thermal convection in a two-dimensional inclined porous layer. High-resolution numerical simulations confirm the emergence of O(1) aspect-ratio large-scale convective rolls, with one natural' roll rotating in the counterclockwise direction and one antinatural' roll rotating in the clockwise direction. As the inclination angle phi is increased, the background mean shear flow intensifies the natural-roll motion, while suppressing the antinatural-roll motion. Our numerical simulations also reveal-for the first time in single-species porous medium convection-the existence of spatially-localized convective states at large phi, which we suggest are enabled by subcritical instability of the base state at sufficiently large inclination angles. To better understand the physics of inclined porous medium convection at different phi, we numerically compute steady convective solutions using Newton iteration and then perform secondary stability analysis of these nonlinear states using Floquet theory. Our analysis indicates that the inclination of the porous layer stabilizes the boundary layers of the natural roll, but intensifies the boundary-layer instability of the antinatural roll. These results facilitate physical understanding of the large-scale cellular flows observed in the numerical simulations at different values of phi.