Modal Selection for Inclined Darcy-Bénard Convection in a Rectangular Cavity

Nonlinear free convection in an inclined rectangular porous cavity heated from below has been studied using a two-dimensional spectral decomposition. The code uses pseudo-arclength continuation to follow solution curves around fold bifurcations. evolution with inclination of the pattern is complicated and it relies strongly on both Darcy–Rayleigh number aspect ratio cavity. When large generally true that only one cell appears, circulation consistent direction buoyancy forces along cooled boundaries. However, as decreases back towards horizontal, this unicellular evolves, sometimes initially via bifurcations, into patterns different numbers cells. Such evolutions always conserve parity cells (such becoming three then five, or two four), but bifurcations also arise between parities. These phenomena are illustrated suitable selection show dependence Nusselt inclination.