Thermal convection in a vertical circular cylinder

Abstract

A theoretical investigation is made of the onset of buoyancy-driven convection in a circular cylinder. Amplitude equations are derived for the weakly nonlinear evolution of critical disturbances at moderate values of the radius-to-height ratio. It is shown that the initial form of the convective motion a t Rayleigh numbers slightly above critical is not axisymmetric. Particular attention is paid to the neighbourhoods of points where two disturbances are simultaneously critical according to linear theory; the nonlinear evolution in such neighbourhoods is studied in detail.