TRANSITION TO UNSTEADY NATURAL-CONVECTION IN A TALL WATER-FILLED CAVITY

The transition to unsteady natural convection in a water-filled differentially heated cavity of vertical aspect ratio 10 is studied numerically by integrating two-dimensional Navier-Stokes equations in the Boussinesq approximation. The numerical algorithm combines a pseudospectral Chebyshev space discretization with a third-order time-stepping scheme. The top and bottom horizontal walls are considered to be either insulated or perfectly conducting. The critical Rayleigh number for adiabatic walls is found to be more than 30 times larger than that corresponding to perfectly conducting walls, in both cases, however, examination of the space-time structure of the temperature and velocity fluctuations shows that the onset of unsteadiness corresponds to boundary layer instability. In the case of perfectly conducting end walls, the transition to unsteady solutions possesses the characteristic features of a supercritical Hopf bifurcation. This is used to accurately determine the critical value. The dependence of the basic oscillation period in the vicinity of the critical Rayleigh number is given. Finally, the influence of unsteadiness on the local heat transfer coefficient is shown. © 1990 American Institute of Physics.