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Prog. Theor. Phys. Vol. 113 No. 1 (2005) pp. 29-53

[ Full Text PDF : FREE ACCESS (253K) ]

Turbulent Transport in Bénard Convection

Hazime Mori,1 Shoichi Kuroki2 and Takehiko Horita3

1Research Institute for Applied Mechanics, Kyushu University, Kasuga 816-8580, Japan
2Fukuoka Women's University, Fukuoka 813-8529, Japan
3Department of Mathematical Informatics, The University of Tokyo, Tokyo 113-8656, Japan

(Received November 8, 2004)

Abstract:

Stochastic evolution equations for turbulent Bénard convection are derived from the Boussinesq equations by transforming the inertial forces into a sum of systematic linear transport terms and random nonlinear fluctuating forces by means of the projection operator method. Then the heat flux and the velocity fluxes of turbulent Bénard convection are formulated in terms of the temperature gradient and the velocity gradient explicitly with turbulent transport coefficients.
It is found that turbulence produces interference between the velocity flux of the vertical velocity component and the heat flux that is similar to the interference between the electric current and the heat flux in the thermoelectric phenomena of metals, so that the heat flux is generated not only by the temperature gradient but also by the velocity gradient. The large-scale flows of turbulent Bénard convection are characterized by this interference effect. It is also shown that a simple scaling law holds for the Rayleigh number and the Prandtl number dependence of the turbulent transport coefficients in the hard turbulence region, as in the case of the scaling law of the Nusselt number discovered by Castaing et al. (1989).


URL : http://ptp.ipap.jp/link?PTP/113/29/
DOI : 10.1143/PTP.113.29

[ Full Text PDF : FREE ACCESS (253K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 116 No. 6 (2006) pp. 1051-1067 :
    The Memory Function and Chaos-Induced Friction in the Chaotic Hénon-Heiles System
    Ryuji Ishizaki, Hazime Mori, Hirotaka Tominaga, Shoichi Kuroki and Nobuyuki Mori

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