Rayleigh-Be´nard Convection in a Small Aspect Ratio Enclosure: Part I—Bifurcation to Oscillatory Convection

Abstract

The present numerical study documents bifurcation sequences for Rayleigh-Be´nard convection in a rectangular enclosure with insulated sidewalls. The aspect ratios are 3.5 and 2.1 and the Boussinesq fluid is water (average temperature of 70°C) with a Prandtl number of 2.5. Two transitions are documented numerically. The first transition is from steady-state to oscillatory flow and the second is a subharmonic bifurcation as the Rayleigh number is increased further. The dynamics of the flow and temperature field is analyzed in detail for the subcritical steady convection and the supercritical oscillatory convection. The numerical results compared well with experiments, both qualitatively and quantitatively.