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

MPG-Autoren
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He,  X.
Laboratory for Fluid Dynamics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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van Gils,  D.
Laboratory for Fluid Dynamics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Bodenschatz,  E.
Laboratory for Fluid Dynamics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Ahlers,  G.
Laboratory for Fluid Dynamics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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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.