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. The transition to chaos observed in the simulations and experiments is similar to the period-doubling (Feigenbaum) route to chaos. However, special symmetry conditions must be imposed numerically, otherwise the route to chaos is different (Ruelle-Takens-Newhouse). In particular, the Feigenbaum route to chaos can be realized only if the oscillating velocity and temperature field preserves the fourfold symmetry that is observed in the mean flow in the horizontal plane.
The present numerical study documents bifurcation sequences for Rayleigh-Benard 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.
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