The stability of axisymmetric convection

The stability of steady axisymmetric solutions of the Rayleigh-Bénard problem to non-axisymmetric disturbances is discussed. In the first part of the paper, the critical Rayleigh numbers for the non-axisymmetric modes of convection in a cylinder are determined. These are found to be lower than the critical Rayleigh number for unbounded convection. In the second part, the stability of finite amplitude axisymmetric solutions is discussed, with particular emphasis on the stability of the flywheel mode. The significance of these results for low Prandtl number convection is briefly discussed, and the connection with solar granulation, in particular the exploding granule phenomenon, is mentioned.