Flow pattern formation and the transition to chaos in a confined container heated locally from below

Experimental and numerical studies on the effects of the Grashof number Gr, and the container height H on the air flow pattern and the bifurcation process to chaos of the roll-cell pattern in a confined rectangular container heated locally from below are presented. The dimensionless container size is 7:3:arbitrary value, where H is the height of the container and D is the width of the centrally heated bottom wall in the short sidewall direction. The flow pattern map which depends on Gr and H/D was obtained mainly by experimentation. Two-dimensional (2D) rolls with their axes parallel to the long sidewalls, in which fluid descending along both cooled long sidewalls is maintained in the same direction, are always produced above both adiabatic bottom walls next to the centrally heated bottom wall. In addition to these two rolls, four types of convective flow patterns above the centrally heated bottom wall are observed: one pair of steady 2D rolls with their axes parallel to the long sidewalls or a similar pair of steady 3D roll-cells in which cell structures exist within the rolls, unsteady 3D cells, and 3D oscillatory flow. For Gr=1.8×106 and H/D=0.20, the 3D roll-cell pattern changes directly from time-dependent sinuous oscillatory motion to chaotic flow. Two positive Lyapunov exponents appear, and the Lyapunov dimension is about 3.7, indicating that this flow may be strongly chaotic. This non-cascade-type transition is due to the sudden flow pattern change from the single pair of the 3D roll-cell to the chaotic cell structure.