### Abstract

We report results of Reynolds-number measurements, based on multi-point temperature measurements and the elliptic approximation (EA) of He and Zhang (2006 Phys. Rev. E 73 055303), Zhao and He (2009 Phys. Rev. E 79 046316) for turbulent Rayleigh-Bénard convection (RBC) over the Rayleigh-number range 10^{11} ≲ Ra ≲ 2 × 10^{14} and for a Prandtl number Pr ≃ 0.8. The sample was a right-circular cylinder with the diameter D and the height L both equal to 112 cm. The Reynolds numbers Re_{U} and Re_{V} were obtained from the mean-flow velocity U and the root-mean-square fluctuation velocity V, respectively. Both were measured approximately at the mid-height of the sample and near (but not too near) the side wall close to a maximum of Re_{U}. A detailed examination, based on several experimental tests, of the applicability of the EA to turbulent RBC in our parameter range is provided. The main contribution to Re_{U} came from a large-scale circulation in the form of a single convection roll with the preferred azimuthal orientation of its down flow nearly coinciding with the location of the measurement probes. First we measured time sequences of Re_{U}(t) and Re_{V}(t) from short (10 s) segments which moved along much longer sequences of many hours. The corresponding probability distributions of Re_{U}(t) and Re_{V}(t) had single peaks and thus did not reveal significant flow reversals. The two averaged Reynolds numbers determined from the entire data sequences were of comparable size. For Ra < Ra_{1}^{∗} ≃ 2 × 10^{13} both Re_{U} and Re_{V} could be described by a power-law dependence on Ra with an exponent ζ close to 0.44. This exponent is consistent with several other measurements for the classical RBC state at smaller Ra and larger Pr and with the Grossmann-Lohse (GL) prediction for Re_{U} (Grossmann and Lohse 2000 J. Fluid. Mech. 407 27; Grossmann and Lohse 2001 86 3316; Grossmann and Lohse 2002 66 016305) but disagrees with the prediction ζ ≃ 0.33 by GL (Grossmann and Lohse 2004 Phys. Fluids 16 4462) for Re_{V}. At Ra = Ra_{2}^{∗} ≃ 7 × 10^{13} the dependence of Re_{V} on Ra changed, and for larger Ra Re_{V} ∼ Ra_{0.50±0.02}, consistent with the prediction for Re_{U} (Grossmann and Lohse 2000 J. Fluid. Mech. 407 27; Grossmann and Lohse Phys. Rev. Lett. 2001 86 3316; Grossmann and Lohse Phys. Rev. E 2002 66 016305; Grossmann and Lohse 2012 Phys. Fluids 24 125103) in the ultimate state of RBC.

Original language | English |
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Article number | 063028 |

Journal | New journal of physics |

Volume | 17 |

Issue number | 6 |

DOIs | |

Publication status | Published - 23 Jun 2015 |

Externally published | Yes |

### Keywords

- elliptic approximation
- Reynolds number
- space-time correlation
- turbulent thermal convection
- ultimate regime

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## Cite this

*New journal of physics*,

*17*(6), [063028]. https://doi.org/10.1088/1367-2630/17/6/063028