Eur. Phys. J. B 21, 295-304 (2001)
https://doi.org/10.1007/s100510170205

Logarithmic corrections to scaling in turbulent thermal convection

CNRS, Groupe Instabilité et Turbulence, CEA/DRECAM/SPEC, 91191 Gif-sur-Yvette Cedex, France and CNRS, Service d'Astrophysique, CE Saclay, 91191 Gif-sur-Yvette Cedex, France and CNRS (UMR 5572) , Observatoire Midi-Pyrénées, 14 avenue Belin, 31400 Toulouse, France

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

Received: 15 December 2000
Revised: 20 March 2001
Published online: 15 May 2001

Abstract

We use a simplified model of turbulent convection to compute analytically heat transport in a horizontal layer heated from below, as a function of the Rayleigh and the Prandtl number. At low Reynolds numbers, when most of the dissipation comes from the mean flow, we recover power classical scaling regimes of the Nusselt versus Rayleigh number, with exponent 1/3 or 1/4. At larger Reynolds number, velocity and temperature fluctuations become non-negligible in the dissipation. In these regimes, there is no exact power law dependence the Nusselt versus Rayleigh or Prandtl. Instead, we obtain logarithmic corrections to the classical soft (exponent 1/3) or ultra-hard (exponent 1/2) regimes, in a way consistent with the most accurate experimental measurements available nowadays. This sets a need for the search of new measurable quantities that are less prone to dimensional theories.