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

Steady and oscillatory instabilities of buoyancy convection in a laterally heated cube with perfectly thermally insulated horizontal boundaries and perfectly thermally conducting 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 1003 to 2563 finite volumes. It is revealed that en route to unsteadiness the flow undergoes a steady symmetry-breaking pitchfork bifurcation, which breaks its reflection and two-dimensional rotational symmetries. With a further increase of the Grashof number, the nonsymmetric flow bifurcates into an oscillatory state via a Hopf bifurcation. It is argued that the steady symmetry-breaking bifurcation takes place owing to the instability of counter-rotating vortical motions. The oscillatory instability develops as a result of the interaction between the unstable boundary layer flow and the stabilizing effect of the stable temperature stratification.