DOI: 10.1140/epjb/e2002-00239-1 THE EUROPEAN PHYSICAL JOURNAL B Scaling in large Prandtl number turbulent thermal convection

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, NuPr−1=2 and Re are a function of RaPr−3=2. At large Reynolds number NuPr1=3 and RePr are function only of RaPr2=3 (within logarithmic corrections). In practice, since Nu is always close to Ra1=3, 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 dierence 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 t of the curve Nu(Ra;Pr) which may be used to describe all measurements at Pr 0:7. PACS. 47.27-i Turbulent flows, convection and heat transfer { 47.27.Eq Turbulence simulation and mod-eling { 47.27.Te Convection and heat transfer 1 Motivation an