The onset and evolution of convection of a fluid completely confined in a vertical cylinder heated from below are investigated.
Having represented three dimensional disturbance field by poloidal potential, the critical Rayleigh numbers are obtained by Galerkin method in a simpler manner than previous works and the weakly nonlinear analysis is performed for a fluid of Prandtl number infinite in a flat cylinder.
It is found that at the weakly nonlinear state, each mode of disturbance with initial small amplitude increase exponentially at first and arrive at the steady state as time increases, and found that the eventual convection structure is basically three parallel roll system, which is consistent with experimental observations.
