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Measurements of Reynolds number near the transition to the ultimate-state of turbulent Rayleigh−Bénard convection

DOI: 10.1615/ICHMT.2012.ProcSevIntSympTurbHeatTransfPal.1440
pages 1403-1406

X. He
Max-Planck Institute for Dynamics and Self Organization (MPIDS), 37077 Göttingen

D. Funfschilling
LSGC CNRS - Nancy Université, 1, rue Grandville, 54001 Nancy Cedex, France

H. Nobach
Max-Planck Institute for Dynamics and Self Organization (MPIDS), 37077 Göttingen

E. Bodenschatz
Institue for Nonlinear Dynamics, University of Gòttingen; Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, D-37077 Gòttingen, Germany; Cornell University, Ithaca, New York

Max-Planck Institute for Dynamics and Self Organization (MPIDS), 37077 Göttingen, Germany; Department of Physics, University of California, Santa Barbara, CA 93106, USA


A Reynolds number Reeff was measured in turbulent Rayleigh-Bénard convection (RBC) of a cylindrical sample over the Rayleigh-number range 1012 ≤ Ra ≤ 1015 and for Prandtl numbers Pr near 0.8 (He et al., 2012). The aspect ratio Γ ≡ D / L of the cylindrical sample was 0.50 (D = 1.12 m was the diameter and L = 2.24 m was the height). The measurements of Reeff were conducted at a distance L/4 above the bottom plate and 1.0 cm away from the sidewall inside the sample. For Ra ≤ 1013 the results showed Reeff α Raζeff with ζeff ≈ 0.43, consistent with classical turbulent RBC. After a transition region for 1013 ≤ Ra ≤ 5×1014, where multi-stability occurred, we found an exponent ζ ≈ 0.50, in agreement with the predictions of Grossmann and Lohse (2011) for the large-Ra asymptotic state. We believe that our measurements revealed the transition of RBC to the ultimate state predicted by Kraichnan (1962).

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