Double diffusive instability in an inclined cavity

Double diffusive convection in a rectangular two-dimensional cavity with imposed temperatures and concentrations along two opposite sidewalls is considered. The study is performed for two-dimensional cavities in which the thermal and solutal buoyancy forces have the same magnitude, but are of opposite sign. The influence on the convective instability of the aspect ratio A (height/length) of the cavity and the cavity inclination α with respect to gravity is discussed. The onset of convection is computed for an infinite layer and compared to that for bounded boxes. The study is completed by the continuation of bifurcating solutions. It is found that, due to centrosymmetry, steady bifurcations are either pitchfork or transcritical depending on A and α. However, a primary pitchfork bifurcation is found to create unstable steady solutions, even if it is the first bifurcation. For the aspect ratios we studied, and close to the onset of convection, the stable solutions are mainly one-roll structures that can be destabilized by further interactions with asymmetric solutions created at primary pitchfork bifurcations. For large aspect ratios, additional asymmetric one-roll solutions are created via more complex branch interactions.