Nonlinear Dynamics of Low-Prandtl Number Rayleigh-Bénard Convection

We present a detailed bifurcation structure and associated flow patterns for lowPrandtl-number (P = 0.005, 0.02) Rayleigh-Bénard convection near its onset. We use both direct numerical simulations and a 30-mode low-dimensional model for this study. The main flow patterns observed for this range are 2D straight rolls, stationary squares, asymmetric squares, oscillating asymmetric squares, relaxation oscillations, and chaos. At the onset of convection, low-P convective flows have stationary 2D rolls and associated stationary and oscillatory asymmetric squares. The range of Rayleigh numbers for which the stationary 2D rolls exist decreases rapidly with decreasing Prandtl numbers and vanishes in the zero-P limit giving rise to chaotic solutions at the onset itself. Our results are in qualitative agreement with results reported earlier on this topic.