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On the relation between Rayleigh-Bénard convection and Lorenz system. (English) Zbl 1084.76026
Summary: Based on an extension of the Lorenz truncation scheme, a chaotic mathematical model is developed to provide a profile of the chaotic attractor associated with the Rayleigh-Bénard convection problem in a plane fluid motion. The attractor of the Lorenz system is a cross-section of the attractor of the proposed model, in which solutions always exist in circles mirroring those appearing in the convection problem.
MSC:
76E06Convection (hydrodynamic stability)
37N10Dynamical systems in fluid mechanics, oceanography and meteorology