DOUBLE-DIFFUSIVE CONVECTION IN A VERTICAL RECTANGULAR CAVITY

In the present work, we study the onset of double diffusive convection in vertical enclosures with equal and opposing buoyancy forces due to horizontal thermal and concentration gradients (in the case Gr(S)/Gr( T)=-1, where Gr(S) and Gr(T) are, respectively, the solutal and therma l Grashof numbers). We demonstrate that the equilibrium solution is li nearly stable until the parameter Ra-T\Le-1\ reaches a critical value, which depends on the aspect ratio of the cell, A. For the square cavi ty we find a critical value of Ra-c\Le-1\=17 174 while previous numeri cal results give a value close to 6000. When A increases, the stabilit y parameter decreases regularly to reach the value 6509, and the wave number reaches a value k(c)=2.53, for A-->infinity. These theoretical results are in good agreement with our direct simulation. We numerical ly Verify that the onset of double diffusive convection corresponds to a transcritical bifurcation point. The subcritical solutions are stro ng attractors, which explains that authors who have worked previously on this problem were not able to preserve the equilibrium solution bey ond a particular value of the thermal Rayleigh number, Ra-o1. This val ue has been confused with the critical Rayleigh number, while it corre sponds in fact to the location of the turning point.