Numerical investigation of Hopf bifurcation corresponding to transition from steady to oscillatory state in a confined convective flow

Onset of oscillatory instability of convection of low-Pradtl-number fluid in a laterally heated rectangular cavity is investigated numerically. Cavities with rigid isothermal vertical boundaries, rigid adiabatic lower boundary, and stressfree adiabatic upper boundary are considered. Critical Grashof numbers corresponding to transition from steady to oscillatory state of the flow are calculated for the aspect ratio veied from 1 to 10. The oscillatory instability is shown to be due to the Hopf bifurcation and is characterized by the frequency of oscillations and pattern of the dominant infinitely small perturbation. Weakly nonlinear analysis of the Hopf bifurcation is used for asymptotic approximations of slightly supercritical flows.