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

##### MPG-Autoren

##### Externe Ressourcen

http://iopscience.iop.org/article/10.1088/1367-2630/17/6/063028/meta

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##### Zitation

He, X., van Gils, D., Bodenschatz, E., & Ahlers, G. (2015). Reynolds numbers and
the elliptic approximation near the ultimate state of turbulent Rayleigh-Bénard convection.* New Journal
of Physics,* *17*(6): 063028. doi:10.1088/1367-2630/17/6/063028.

Zitierlink: http://hdl.handle.net/11858/00-001M-0000-0029-7F72-B

##### Zusammenfassung

Wereport 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 samplewas a
right-circular cylinder with the diameterDand the height L both equal to 112 cm. The Reynolds
numbers ReU and ReV were obtained from the mean-flow velocityUand 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 10
< * ≃ × 13 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 disagreeswith the prediction ζ ≃ 0.33 by
GL (Grossmann and Lohse 2004 Phys. Fluids 16 4462) for ReV. At Ra Ra2 7 10
= * ≃ × 13 the
dependence of ReV on Ra changed, and for larger Ra ReV Ra
∼ 0.50±0.02, consistentwith 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.