Oscillatory instability of 2D natural convection flow in a square enclosure with a tandem of vertically aligned cylinders

The oscillatory instability of 2D natural convection flow in a cooled square enclosure with a tandem of vertically aligned cylinders was investigated in detail. The study was performed by applying linear stability analysis and time integration of slightly perturbed flows. As a function of the distance between the two cylinders the flow underwent a transition to unsteadiness via either a symmetry-breaking or a symmetry-preserving first Hopf bifurcation. The critical values of the Rayleigh number Ra _cr and the oscillatory instability ω _cr for the transition to unsteadiness were accurately estimated. An extensive discussion of the scenarios determining the mechanisms driving the onset of the observed instabilities is presented.