The Lorenz model for Rayleigh-Bénard convection is extended to the five components model taking an autonomous shear flow effect into account. The five components model is numerically solved and analyzed in detail. Based on the Lyapunov exponent analysis , how the introduction of the new degrees of the freedom (the shear flow) changes the chaotic behavior of the solution is examined. The attractors, the time evolutions, the power spectra, the Nusselt number of the five components model are compared with those of the Lorenz model. It is found that the solutions of both models converge to the same one when the Rayleigh number is small. When the Rayleigh number exceeds a critical value, the difference between the Lorenz model and the five components model is observed, i.e., the former has only the periodic solutions, while the latter contains the chaotic solutions. Some examples are shown. The limitation to a model with a few degrees of freedom is also discussed.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)