Different routes to chaos in low Prandtl-number Rayleigh–Bénard convection

Abstract

We investigate transition to chaos in Rayleigh–Bénard convection (RBC) of low Prandtl-number fluids with free-slip boundary conditions. Detailed three dimensional direct numerical simulations (DNS) of the governing equations of RBC are performed for this purpose. DNS for Pr=0.025 shows two possible routes to chaos, namely via period doubling route and quasiperiodic route. A low dimensional model is constructed using the DNS data and it helps us to understand the bifurcation structure associated with different routes to chaos. Bifurcation analysis of the model also shows two distinct route to chaos for Pr=0.025, similar to DNS, viz. period doubling and quasiperiodic route to chaos. Period doubling route is associated with the periodic wavy rolls solution while the quasiperiodic route is associated with the stationary squares solutions. The results of our investigation show similarity with previous experimental observations of Fauve and Libchabar (1981) [1]. We also investigate the bifurcation structure near the onset of convection for Pr=0.3 using the same low dimensional model. The investigation shows that the route to chaos is quasiperiodic in this case and found to match well with DNS results.