Double-diffusive convection in a circular cylinder (Q1092741)

A theoretical study is made of the onset of steady double-diffusive convection in a circular cylinder of small to moderate aspect ratio. An eigenfunction expansion method is used to derive systems of amplitude equations for weakly nonlinear evolution of critical disturbances. It is shown that the nature of the convective solution near criticality depends strongly on the cylinder's aspect ratio; this is particularly the case at or near aspect ratios where two modes become unstable at the same Rayleigh number. There is also a strong dependence on Prandtl number, which is disussed.