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Turbulent convection at very high Rayleigh numbers

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An Erratum to this article was published on 27 July 2000

Abstract

Turbulent convection occurs when the Rayleigh number (Ra)—which quantifies the relative magnitude of thermal driving to dissipative forces in the fluid motion—becomes sufficiently high. Although many theoretical and experimental studies of turbulent convection exist, the basic properties of heat transport remain unclear. One important question concerns the existence of an asymptotic regime that is supposed to occur at very high Ra. Theory predicts that in such a state the Nusselt number (Nu), representing the global heat transport, should scale as Nu ∝ Raβ with β = 1/2. Here we investigate thermal transport over eleven orders of magnitude of the Rayleigh number (106 ≤ Ra ≤ 1017), using cryogenic helium gas as the working fluid. Our data, over the entire range of Ra, can be described to the lowest order by a single power-law with scaling exponent β close to 0.31. In particular, we find no evidence for a transition to the Ra1/2 regime. We also study the variation of internal temperature fluctuations with Ra, and probe velocity statistics indirectly.

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Figure 1: A schematic view of the experimental apparatus.
Figure 2: Log–log plot of the Nusselt number (Nu) versus Rayleigh number (Ra).
Figure 3: The probability density function (PDF) of the temperature fluctuations in the centre of the cell measured at different Ra as indicated.
Figure 4: The power spectral density (PSD) of the temperature fluctuations in the cell measured at Ra = 6 × 1011.
Figure 5: A rough measure of the large-scale velocity in the cell.

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Acknowledgements

We thank M. McAshan for his assistance in the design of the cryostat, and many colleagues for useful discussions. This research was supported by the US National Science Foundation.

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Authors and Affiliations

  1. Cryogenic Helium Turbulence Laboratory Department of Physics, University of Oregon, Eugene, 97403, Oregon, USA

    J. J. Niemela, L. Skrbek, K. R. Sreenivasan & R. J. Donnelly

  2. Mason Laboratory, Yale University , New Haven, 06520-8286, Connecticut, USA

    K. R. Sreenivasan

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  1. J. J. Niemela
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  2. L. Skrbek
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  3. K. R. Sreenivasan
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  4. R. J. Donnelly
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Correspondence to K. R. Sreenivasan.

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Niemela, J., Skrbek, L., Sreenivasan, K. et al. Turbulent convection at very high Rayleigh numbers. Nature 404, 837–840 (2000). https://doi.org/10.1038/35009036

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