Patterns and bifurcations in low–Prandtl-number Rayleigh-Bénard convection

¹  Department of Physics, Indian Institute of Technology - Kanpur, India
²  Department of Mechanical Engineering, Indian Institute of Technology - Kanpur, India

Corresponding author: wahi@iitk.ac.in

Received: 4 December 2009
Accepted: 9 February 2010

Abstract

We present a detailed bifurcation structure and associated flow patterns for low–Prandtl-number (P=0.0002, 0.002, 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. We observe that low–Prandtl-number (low-P) convection exhibits similar patterns and chaos as zero-P convection (Pal P. et al., EPL, 87 (2009) 04003) namely 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 in contrast to zero-P convection where chaos appears at the onset itself. The range of Rayleigh number for which stationary 2D rolls exist decreases rapidly with decreasing Prandtl number. Our results are in qualitative agreement with results reported earlier.