Bifurcations and chaos in large-Prandtl number Rayleigh–Bénard convection

Abstract

Rayleigh–Bénard convection with large-Prandtl number (P) is studied using a low-dimensional model constructed with the energetic modes of pseudospectral direct numerical simulations. A detailed bifurcation analysis of the non-linear response has been carried out for water at room temperature (P=6.8) as the working fluid. This analysis reveals a rich instability and chaos picture: steady rolls, time-periodicity, quasiperiodicity, phase locking, chaos, and crisis. Our low-dimensional model captures the reappearance of ordered states after chaos, as previously observed in experiments and simulations. We also observe multiple coexisting attractors consistent with previous experimental observations for a range of parameter values. The route to chaos in the model occurs through quasiperiodicity and phase locking, and attractor-merging crisis. Flow patterns spatially moving along the periodic direction have also been observed in our model.