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

Abstract

A sequence of three steady - oscillatory transitions of buoyancy convection of air in a laterally heated cube with perfectly thermally insulated horizontal and spanwise boundaries is studied. The problem is treated by Newton and Arnoldi methods based on Krylov subspace iteration. The finite volume grid is gradually refined from 100^3 to 256^3 finite volumes. It is shown that the primary instability is characterized by two competing eigenmodes, whose temporal development results in two different oscillatory states that differ by their symmetries. Bifurcations due to both modes are subcritical. These modes develop into different oscillatory and then stochastic flow states, which, at larger Grashof number, stabilize and arrive to single stable steady flow. With further increase of the Grashof number this flow loses it stability again. It is argued that in all the three transitions, the instabilities onsets, as well as reinstatement of stability, take place owing to an interaction between a destabilizing centrifugal mechanism and stabilizing effect of thermal stratification.