Instabilities of flows between differentially rotating coaxial vertical cylinders in the presence of a radial temperature gradient

The problem of the transition from the basic cylindrically symmetric state of flow to secondary axisymmetric and non-axisymmetric flows is investigated in the limit of a small gap between the coaxial cylindrical boundaries which are kept at different temperatures. In addition to the mechanism for the onset of Taylor vortices other mechanisms depending on the buoyancy associated with the axially oriented gravity and on the shear of the vertical component of the basic velocity field must be considered in the interpretation of the numerical results. The linear stability analysis is extended into the weakly nonlinear regime. Regions of subcritical onset of vortices will be important in a comparison between theoretical results of linear theory and experimental measurements.