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Prandtl and Rayleigh number dependence of heat transport in high Rayleigh number thermal convection

Published online by Cambridge University Press:  24 October 2011

Richard J. A. M. Stevens ,
Detlef Lohse  and
Roberto Verzicco
Richard J. A. M. Stevens*
Affiliation:
Department of Science and Technology and J.M. Burgers Center for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
Detlef Lohse
Affiliation:
Department of Science and Technology and J.M. Burgers Center for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
Roberto Verzicco
Affiliation:
Department of Science and Technology and J.M. Burgers Center for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands Department of Mechanical Engineering, Universitá di Roma ‘Tor Vergata’, Via del Politecnico 1, 00133, Roma
*
†Email address for correspondence: r.j.a.m.stevens@tnw.utwente.nl
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Abstract

Results from direct numerical simulation for three-dimensional Rayleigh–Bénard convection in samples of aspect ratio and up to Rayleigh number are presented. The broad range of Prandtl numbers is considered. In contrast to some experiments, we do not see any increase in with increasing , neither due to an increasing , nor due to constant heat flux boundary conditions at the bottom plate instead of constant temperature boundary conditions. Even at these very high , both the thermal and kinetic boundary layer thicknesses obey Prandtl–Blasius scaling.

JFM classification

Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent convection
Type
Papers
Information
Journal of Fluid Mechanics , Volume 688 , 10 December 2011 , pp. 31 - 43
Copyright
Copyright © Cambridge University Press 2011

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Stevens et al. supplementary movies

Movie of the temperature field in a vertical cut for the simulation at Ra = 2 x 1012 and Pr = 0.7 in an aspect ratio Γ = 0.5 sample. The dimensionless time is indicated in the top of the movie.

Download Stevens et al. supplementary movies(Video)
Video 39.7 MB

Stevens et al. supplementary movies

Movie of the temperature field in a vertical cut for the simulation at Ra = 2 x 1012 and Pr = 0.7 in an aspect ratio Γ = 0.5 sample. The dimensionless time is indicated in the top of the movie.

Download Stevens et al. supplementary movies(Video)
Video 9.9 MB

Stevens et al. supplementary movies

Movie of the vertical velocity field in a vertical cut for the simulation at Ra = 2 x 1012 and Pr = 0.7 in an aspect ratio Γ = 0.5 sample. The dimensionless time is indicated in the top of the movie.

Download Stevens et al. supplementary movies(Video)
Video 40.4 MB

Stevens et al. supplementary movies

Movie of the vertical velocity field in a vertical cut for the simulation at Ra = 2 x 1012 and Pr = 0.7 in an aspect ratio Γ = 0.5 sample. The dimensionless time is indicated in the top of the movie.

Download Stevens et al. supplementary movies(Video)
Video 9.9 MB

Stevens et al. supplementary movies

Movie of the temperature field in a vertical cut for the simulation at Ra = 2 x 1012 and Pr = 0.7 in an aspect ratio Γ = 0.5 sample. The dimensionless time is indicated in the top of the movie. This vertical cut is perpendicular to the plane shown in movie 1.

Download Stevens et al. supplementary movies(Video)
Video 34.2 MB

Stevens et al. supplementary movies

Movie of the temperature field in a vertical cut for the simulation at Ra = 2 x 1012 and Pr = 0.7 in an aspect ratio Γ = 0.5 sample. The dimensionless time is indicated in the top of the movie. This vertical cut is perpendicular to the plane shown in movie 1.

Download Stevens et al. supplementary movies(Video)
Video 8.6 MB

Stevens et al. supplementary movies

Movie of the vertical velocity field in a vertical cut for the simulation at Ra = 2 x 1012 and Pr = 0.7 in an aspect ratio Γ = 0.5 sample. The dimensionless time is indicated in the top of the movie. This vertical cut is perpendicular to the plane shown in movie 2.

Download Stevens et al. supplementary movies(Video)
Video 35.4 MB

Stevens et al. supplementary movies

Movie of the vertical velocity field in a vertical cut for the simulation at Ra = 2 x 1012 and Pr = 0.7 in an aspect ratio Γ = 0.5 sample. The dimensionless time is indicated in the top of the movie. This vertical cut is perpendicular to the plane shown in movie 2.

Download Stevens et al. supplementary movies(Video)
Video 8.6 MB

Stevens et al. supplementary movies

Movie of the temperature in three horizontal planes (0:25z/L, 0:50z/L, and 0:75z/L) for the simulation at Ra = 2 x 1012 and Pr = 0.7 in an aspect ratio Γ = 0.5 sample. The dimensionless time is indicated in the top of the movie.

Download Stevens et al. supplementary movies(Video)
Video 50.7 MB

Stevens et al. supplementary movies

Movie of the temperature in three horizontal planes (0:25z/L, 0:50z/L, and 0:75z/L) for the simulation at Ra = 2 x 1012 and Pr = 0.7 in an aspect ratio Γ = 0.5 sample. The dimensionless time is indicated in the top of the movie.

Download Stevens et al. supplementary movies(Video)
Video 9.9 MB

Stevens et al. supplementary movies

Movie of the vertical velocity field in three horizontal planes (0:25z/L, 0:50z/L, and 0:75z/L) for the simulation at Ra = 2 x 1012 and Pr = 0.7 in an aspect ratio Γ = 0.5 sample. The dimensionless time is indicated in the top of the movie.

Download Stevens et al. supplementary movies(Video)
Video 52.3 MB

Stevens et al. supplementary movies

Movie of the vertical velocity field in three horizontal planes (0:25z/L, 0:50z/L, and 0:75z/L) for the simulation at Ra = 2 x 1012 and Pr = 0.7 in an aspect ratio Γ = 0.5 sample. The dimensionless time is indicated in the top of the movie.

Download Stevens et al. supplementary movies(Video)
Video 9.9 MB