3-DIMENSIONAL INSTABILITY OF AXISYMMETRICAL BUOYANT CONVECTION IN CYLINDERS HEATED FROM BELOW

The stability of steady axisymmetric convection in cylinders heated fr om below and insulated laterally is investigated numerically using a m ixed finite-difference/Chebyshev collocation method to solve the base flow and the linear stability equations. Linear stability boundaries a re given for radius to height ratios Gamma from 0.9 to 1.56 and for Pr andtl numbers Pr = 0.02 and Pr = 1. Depending on Gamma and Pr, the azi muthal wavenumber of the critical mode may be m = 1, 2, 3, or 4. The d ependence of the critical Rayleigh number on the aspect ratio and the instability mechanisms are explained by analysing the energy transfer to the critical modes for selected cases. In addition to these results the onset of buoyant convection in liquid bridges with stress-free co nditions on the cylindrical surface is considered. For insulating ther mal boundary conditions, the onset of convection is never axisymmetric and the critical azimuthal wavenumber increases monotonically with Ga mma. The critical Rayleigh number is less then 1708 for most aspect ra tios.