Transition to chaos in the Rayleigh-Benard convection

Direct numerical simulations of the Rayleigh-Benard convection in a rectang ular box ar a run using the MAC method at the assigned values of the extern al parameters such that the Prandtl number Pr = 5 and the box aspect ratios Gamma(x) = 3.5 and Gamma(y) = 2. The grid consists of 84 x 38 x 24 uniform ly divided cubic cells. The results show that with increase of the Rayleigh number the oscillatory motion undergoes successive transitions in such a w ay as mono-periodic --> bi-periodic --> frequency-locked state --> chaotic, which are in favorable agreement with the available experimental results d ue to Gollub and Benson obtained under the same settup of the external para meters Pr, Gamma(x), and Gamma(y).