ON OSCILLATORY INSTABILITY OF CONVECTIVE FLOWS AT LOW PRANDTL NUMBER

Numerical investigation of the oscillatory instability of convective f lows in laterally heated rectangular cavities is presented. Cavities w ith no-slip isothermal vertical boundaries, no-slip adiabatic lower bo undary, and stress-free adiabatic upper boundary are considered. Depen dence of the critical Grashof number and the critical frequency of osc illations on the aspect ratio (A = length/height) of the cavity are in vestigated The stability diagrams were obtained for the whole interval of the aspect ratio 1 less than or equal to A less than or equal to 1 0. The study was carried out for two values of the Prandtl number, Pr = 0 and 0.015. It was shown that the oscillatory instability sets in a s a result of the Hopf bifurcation. It was found that at two different values of the Prandtl number considered the instability is caused by different infinitely small dominant perturbations, which means that th e convective heat transfer strongly affects stability of the flow even for cases having small Prandtl number. No asymptotic behavior large a spect ratios was found up to A = 10. Slightly supercritical oscillator y flows were approximated asymptotically by means of the weakly nonlin ear analysis of the calculated bifurcation.