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Chen, Zhi-Min; Price, W. G.

On the relation between Rayleigh-Bénard convection and Lorenz system. (English) Zbl 1084.76026

Chaos Solitons Fractals 28, No. 2, 571-578 (2006).
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.

Cited in 11 Documents

MSC:

76E06 Convection in hydrodynamic stability
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology

Keywords:

chaotic attractor
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\textit{Z.-M. Chen} and \textit{W. G. Price}, Chaos Solitons Fractals 28, No. 2, 571--578 (2006; Zbl 1084.76026)
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References:

[1] Lorenz, E.N., Deterministic nonperiodic flow, J atmos sci, 20, 130-141, (1963) · Zbl 1417.37129
[2] Ruelle, D.; Takens, F., On the nature of turbulence, Commun math phys, 20, 167-192, (1971) · Zbl 0223.76041
[3] Li, T.Y.; Yorke, J.A., Period three implies chaos, Am math monthly, 82, 985-992, (1975) · Zbl 0351.92021
[4] El Naschie, M.S.; Elnashaie, S.S.E.H., The connection between fluid and elastostatical turbulence, Math comput model, 15, 17-23, (1991) · Zbl 0753.76079
[5] El Naschie, M.S., Soliton chaos modes for mechanical and biological elastic chains, Phys lett A, 147, 275-281, (1990)
[6] El Naschie, M.S.; Al Athel, S.; Kapitaniak, T., A note on elastic turbulence and diffusion, J sound vib, 155, 515-522, (1992)
[7] Chandrasekhar, S., Hydrodynamic and hydromagnetic stability, (1961), Clarendon Press Oxford · Zbl 0142.44103
[8] Getling, A.V., Rayleigh-Bénard convection, (1998), World Scientific Singapore · Zbl 0910.76001
[9] Bénard, H., LES tourbillons cellulaires dans une nappe liquide, Rev Gén sci pure appl, 11, 1261-1271, (1900)
[10] Bénard, H., LES tourbillons cellulaires dans une nappe liquide, Rev Gén sci pure appl, 11, 1309-1328, (1900)
[11] Rayleigh, L., On convection currents in a horizontal layer of fluid, when the higher temperature is on the under side, Philos mag, 32, 529-546, (1916) · JFM 46.1249.04
[12] Saltzman, B., Finite amplitude free convection as an initial value problem—I, J atmos sci, 19, 329-341, (1962)
[13] Ma, T.; Wang, S., Dynamic bifurcation and stability in Rayleigh-Bénard convection, Commun math sci, 2, 159-183, (2004) · Zbl 1133.76315
[14] Sparrow, C., The Lorenz equations: bifurcations, chaos, and strange attractors, (1982), Springer New York · Zbl 0504.58001
[15] Chen, Z.-M., A note on kaplan-Yorke-type estimates on the fractal dimension of chaotic attractors, Chaos, solitons & fractals, 3, 575-582, (1993) · Zbl 0783.58044
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