Transitions of natural convection in a vertical fluid layer

Transitions of natural convection in a vertical fluid layer contained in a tall cavity with differentially heated side walls are investigated numerically and theoretically. Steady-state solutions are calculated by solving the steady-state equations numerically and their stability is investigated by applying the linear stability theory. It is found that the bifurcation structure of the steady-state solution consists of smooth transition and saddle-node branches and that the change in flow pattern occurs without any instabilities along the smooth transition branch, whereas transitions from the saddle-node branch to the smooth transition branch may happen which accompany the change of flow pattern.