Reynolds numbers and the elliptic approximation near the ultimate state of turbulent Rayleigh-Bénard convection

Xiaozhou He, Dennis P.M. Van Gils, Eberhard Bodenschatz, Guenter Ahlers

Research output: Contribution to journalArticleAcademicpeer-review

17 Citations (Scopus)
5 Downloads (Pure)

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 1011 ≲ Ra ≲ 2 × 1014 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 ReU and ReV 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 ReU. 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 ReU 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 ReU(t) and ReV(t) from short (10 s) segments which moved along much longer sequences of many hours. The corresponding probability distributions of ReU(t) and ReV(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 < Ra1 ≃ 2 × 1013 both ReU and ReV 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 ReU (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 ReV. At Ra = Ra2 ≃ 7 × 1013 the dependence of ReV on Ra changed, and for larger Ra ReV ∼ Ra0.50±0.02, consistent with the prediction for ReU (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 languageEnglish
Article number063028
JournalNew journal of physics
Volume17
Issue number6
DOIs
Publication statusPublished - 23 Jun 2015
Externally publishedYes

Keywords

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

Fingerprint Dive into the research topics of 'Reynolds numbers and the elliptic approximation near the ultimate state of turbulent Rayleigh-Bénard convection'. Together they form a unique fingerprint.

  • Cite this