Bifurcation of natural convection flow in an inclined differentially heated closed square cavity

The natural convection flow in an inclined differentially heated cavity is investigated numerically with two-dimensional simulations at Rayleigh number Ra = 1 x 10(7) and Ra = 1 x 10(8) for Prandtl number Pr = 7.0. At theta = 0, the problem is the standard canonical differentially heated cavity flow with isothermal "hot" and "cold" vertical walls and with adiabatic horizontal walls. As the angle of inclination is increased, with the hot wall situated below the cold wall, the flow approaches an unstable Rayleigh-Bernard type flow. Below a critical angle the fully developed flow is steady and exhibits the same basic structure of the standard cavity flow. As the angle of inclination is increased, the flow undergoes a bifurcation so that the fully developed flow is unsteady and single mode. The bifurcation takes the form of traveling waves continually circulating the periphery of the cavity. These waves are supported by convectively unstable natural convection boundary layers on the heated/cooled walls and by attached plumes on the adiabatic walls. It is the establishment of these plumes coupling the opposing boundary layers which provides the mechanism for absolutely unstable flow