The convection in an annular container with heated bottom,cooled top and insulated side walls are studied by both linear instability analysis and direct numerical simulation.The onset of convection is investigated by linear stability analysis and corresponding pattern selection mechanisms are discussed.The nonlinear evolution of different flow patterns and the convective heat transfer are simulated.The transition to oscillatory flow is also given by stability analysis where the base flow is a steady three dimensional flow.The stability predictions are in good agreement with the numerical simulations,including both the growth rate and the dimensionless frequency.
