Transition routes of natural convection in a vertical fluid layer

Transition routes of natural convection in a vertical fluid layer contained in a tall cavity with differentially heated side walls are investigated theoretically on the assumption of two-dimensional flow field. Steady-state solutions are calculated by solving the steady-state equations numerically, and their stability is investigated by applying the linear stability theory. Periodic-state solutions are also obtained by numerical simulations. Bifurcation diagram of the steady- and periodic-state solutions is obtained and the routes of transition of the natural convection reported so far are interpreted according to the diagram. It is found that the bifurcation diagram is very complicated in a limited range of the Rayleigh number, whereas it is quite simple out of the range. The dependence of heat transfer between the two vertical walls on the flow pattern of the convection is also discussed.