BIFURCATION TO UNSTEADY NATURAL CONVECTION FOR AIR AND WATER IN A CAVITY HEATED FROM THE SIDE
The stability of the steady laminar natural-convection flow of air (Prandtl number 0.71) and water (Prandtl number 7.0) in a square cavity is calculated by numerically solving the unsteady, two-dimensional Navier-Stokes equations. The cavity has a hot and cold vertical wall and either conducting or adiabatic horizontal walls. The flow looses its stability at a lower Rayleigh number in the case of conducting horizontal walls than in the case of adiabatic horizontal walls. The flow of water is more stable than the flow of air. Directly above the critical Rayleigh number the unsteady now shows a single-frequency oscillation. Air in the case of adiabatic horizontal walls is an exception and shows two frequencies. The instabilities in the cavity seem to be related to well-known elementary instability mechanisms.