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A sequence of three steady - oscillatory transitions of buoyancy convectionof air in a laterally heated cube with perfectly thermally insulated horizontaland spanwise boundaries is studied. The problem is treated by Newton andArnoldi methods based on Krylov subspace iteration. The finite volume grid isgradually refined from 100^3 to 256^3 finite volumes. It is shown that theprimary instability is characterized by two competing eigenmodes, whosetemporal development results in two different oscillatory states that differ bytheir symmetries. Bifurcations due to both modes are subcritical. These modesdevelop into different oscillatory and then stochastic flow states, which, atlarger Grashof number, stabilize and arrive to single stable steady flow. Withfurther increase of the Grashof number this flow loses it stability again. Itis argued that in all the three transitions, the instabilities onsets, as wellas reinstatement of stability, take place owing to an interaction between adestabilizing centrifugal mechanism and stabilizing effect of thermalstratification.

Sequence of bifurcations of natural convection of air in a laterally heated cube with perfectly insulated horizontal and spanwise boundaries