Eur. Phys. J. B 28, 361-367 (2002)
https://doi.org/10.1140/epjb/e2002-00239-1

Scaling in large Prandtl number turbulent thermal convection

CNRS, Groupe Instabilité et Turbulence, CEA/DSM/DRECAM/SPEC, 91191 Gif-sur-Yvette Cedex, France

Corresponding author: ^a bdubru@discovery.saclay.cea.fr

Received: 27 February 2002
Revised: 29 May 2002
Published online: 31 July 2002

Abstract

We study the scaling properties of heat transfer Nu in turbulent thermal convection at large Prandtl number Pr using a quasi-linear theory. We show that two regimes arise, depending on the Reynolds number Re. At low Reynolds number, and Re are a function of . At large Reynolds number and Re Pr are function only of (within logarithmic corrections). In practice, since Nu is always close to , this corresponds to a much weaker dependence of the heat transfer in the Prandtl number at low Reynolds number than at large Reynolds number. This difference may solve an existing controversy between measurements in SF₆ (large Re) and in alcohol/water (lower Re). We link these regimes with a possible global bifurcation in the turbulent mean flow. We further show how a scaling theory could be used to describe these two regimes through a single universal function. This function presents a bimodal character for intermediate range of Reynolds number. We explain this bimodality in term of two dissipation regimes, one in which fluctuation dominate, and one in which mean flow dominates. Altogether, our results provide a six parameters fit of the curve Nu(Ra,Pr) which may be used to describe all measurements at .