Prog. Theor. Phys. Vol. 113 No. 1 (2005) pp. 29-53
Turbulent Transport in Bénard Convection
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)
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
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).
DOI : 10.1143/PTP.113.29
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Citing Article(s) :
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