Double diffusive instability in an inclined cavity

Double diffusive convection in a rectangular two-dimensional cavity with im posed temperatures and concentrations along two opposite sidewalls is consi dered. The study is performed for two-dimensional cavities in which the the rmal and solutal buoyancy forces have the same magnitude, but are of opposi te sign. The influence on the convective instability of the aspect ratio A (height/length) of the cavity and the cavity inclination a with respect to gravity is discussed. The onset of convection is computed for an infinite l ayer and compared to that for bounded boxes. The study is completed by the continuation of bifurcating solutions. It is found that, due to centrosymme try, steady bifurcations are either pitchfork or transcritical depending on A and cu. However, a primary pitchfork bifurcation is found to create unst able steady solutions, even if it is the first bifurcation. For the aspect ratios we studied, and close to the onset of convection, the stable solutio ns are mainly one-roll structures that can be destabilized by further inter actions with asymmetric solutions created at primary pitchfork bifurcations . For large aspect ratios, additional asymmetric one-roll solutions are cre ated via more complex branch interactions. (C) 1999 American Institute of P hysics. [S1070-6631(99)01603-7].