Instabilities and chaos in low-Prandtl number rayleigh-Bénard convection

We investigate instabilities and chaos in Rayleigh-Bénard convection (RBC) of low Prandtl-number (Pr) fluids with stress-free boundary conditions. Three dimensional direct numerical simulations (DNS) of the governing equations of RBC are done for investigation. DNS shows the existence of multiple solutions near the onset of convection. To understand the origin of these solutions and their bifurcations, we construct a low dimensional model from the DNS data. The low dimensional model unfolds a rich bifurcation structure in RBC of low Prandtl-number fluids. The bifurcation structure involves various bifurcations including pitchfork, Neimark-Sacker, Homoclinic gluing, Hopf bifrucations, and attractor merging crisis near the onset of convection. The results of the model are consistent with that of the DNS.