Bifurcations in two-dimensional Rayleigh-Bénard convection

Abstract

Two-dimensional bouyancy-driven convection in a horizontal fluid layer with stress-free boundary conditions at top and bottom and periodic boundary conditions in the horizontal direction is investigated by means of numerical simulation and bifurcation-analysis techniques. As the bouyancy forces increase, the primary stationary and symmetric convection rolls undergo successive Hopf bifurcations, bifurcations to traveling waves, and phase lockings. We pay attention to symmetry breaking and its connection with the generation of large-scale horizontal flows. Calculations of Lyapunov exponents indicate that at a Rayleigh number of $2.3\ifmmode\times\else\texttimes\fi{}{10}^{5}$ no temporal chaos is reached yet, but the system moves nonchaotically on a 4-torus in phase space.