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Experimental investigation of longitudinal space–time correlations of the velocity field in turbulent Rayleigh–Bénard convection

Published online by Cambridge University Press:  02 August 2011

Quan Zhou ,
Chun-Mei Li ,
Zhi-Ming Lu  and
Yu-Lu Liu
Quan Zhou*
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China Shanghai Key Laboratory of Mechanics in Energy and Environment Engineering, Shanghai University, Shanghai 200072, China Modern Mechanics Division, E-Institutes of Shanghai Universities, Shanghai University, Shanghai 200072, China
Chun-Mei Li
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
Zhi-Ming Lu
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China Shanghai Key Laboratory of Mechanics in Energy and Environment Engineering, Shanghai University, Shanghai 200072, China Modern Mechanics Division, E-Institutes of Shanghai Universities, Shanghai University, Shanghai 200072, China
Yu-Lu Liu
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
*
†Email address for correspondence: qzhou@shu.edu.cn
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Abstract

We report an experimental investigation of the longitudinal space–time cross-correlation function of the velocity field, , in a cylindrical turbulent Rayleigh–Bénard convection cell using the particle image velocimetry (PIV) technique. We show that while Taylor’s frozen-flow hypothesis does not hold in turbulent thermal convection, the recent elliptic model advanced for turbulent shear flows (He & Zhang, Phys. Rev. E, vol. 73, 055303) is valid for the present velocity field for all over the cell, i.e. the isocorrelation contours of the measured have an elliptical curve shape and hence can be related to via with and being two characteristic velocities. We further show that the fitted is proportional to the mean velocity of the flow, but the values of are larger than the theoretical predictions. Specifically, we focus on two representative regions in the cell: the region near the cell sidewall and the cell’s central region. It is found that and are approximately the same near the sidewall, while at the cell centre.

JFM classification

Convection: Convection Turbulent Flows: Turbulent convection
Type
Papers
Information
Journal of Fluid Mechanics , Volume 683 , 25 September 2011 , pp. 94 - 111
Copyright
Copyright © Cambridge University Press 2011

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References

1. Ahlers, G., Brown, E. & Nikolaenko, A. 2006 The search for slow transient, and the effect of imperfect vertical alignment, in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 557, 347–367.CrossRefGoogle Scholar
2. Ahlers, G., Grossmann, S. & Lohse, D. 2009 Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81, 503–537.CrossRefGoogle Scholar
3. Calzavarini, E., Toschi, F. & Tripiccione, R. 2002 Evidences of Bolgiano–Obhukhov scaling in three-dimensional Rayleigh–Bénard convection. Phys. Rev. E 66, 016304.CrossRefGoogle ScholarPubMed
4. Frisch, U. 1995 Turbulence. Cambridge University Press.CrossRefGoogle Scholar
5. He, X.-Z., He, G.-W. & Tong, P. 2010 Small-scale turbulent fluctuations beyond Taylor’s frozen-flow hypothesis. Phys. Rev. E 81, 065303(R).CrossRefGoogle ScholarPubMed
6. He, X.-Z. & Tong, P. 2011 Kraichnan’s random sweeping hypothesis in homogeneous turbulent convection. Phys. Rev. 83, 037302.Google ScholarPubMed
7. He, G.-W. & Zhang, J.-B. 2006 Elliptic model for space–time correlations in turbulent shear flows. Phys. Rev. E 73, 055303(R).CrossRefGoogle ScholarPubMed
8. Jachens, A., Schumachder, J., Eckhardt, B., Knobloch, K. & Fernholz, H. H. 2006 Asymmetry of temporal cross-correlations in turbulent shear flows. J. Fluid Mech. 547, 55–64.CrossRefGoogle Scholar
9. Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk. SSSR 30, 299–303.Google Scholar
10. Kraichnan, R. H. 1964 Kolmogorov’s hypotheses and Eulerian turbulence theory. Phys. Fluids 7, 1723–1734.CrossRefGoogle Scholar
11. Lohse, D. & Xia, K.-Q. 2010 Small-scale properties of turbulent Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 42, 335–364.CrossRefGoogle Scholar
12. Lumley, J. L. 1965 Interpretation of time spectra measured in high-intneisty shear flows. Phys. Fluids 8, 1056–1062.CrossRefGoogle Scholar
13. Pinton, J.-F. & Labbe, R. 1994 Correction of the Taylor hypothesis in swirling flows. J. Phys. II (Paris) 4, 1461–1468.Google Scholar
14. Qiu, X.-L., Shang, X.-D., Tong, P. & Xia, K.-Q. 2004 Velocity oscillations in turbulent Rayleigh–Bénard convection. Phys. Fluids 16, 412–423.CrossRefGoogle Scholar
15. Qiu, X.-L. & Tong, P. 2001 Large-scale velocity structures in turbulent thermal convection. Phys. Rev. E 64, 036304.CrossRefGoogle ScholarPubMed
16. Qiu, X.-L. & Tong, P. 2002 Temperature oscillations in turbulent Rayleigh–Bénard convection. Phys. Rev. E 66, 026308.CrossRefGoogle ScholarPubMed
17. Shang, X.-D. & Xia, K.-Q. 2001 Scaling of the velocity power spectra in turbulent thermal convection. Phys. Rev. E 64, 065301(R).CrossRefGoogle ScholarPubMed
18. Sreenivasan, K. R. & Antonia, R. A. 1997 The phenomenology of small-scale turbulence. Annu. Rev. Fluid Mech. 29, 435–472.CrossRefGoogle Scholar
19. Sun, C., Ren, L.-Y., Song, H. & Xia, K.-Q. 2005a Heat transport by turbulent Rayleigh–Bénard convection in 1 m diameter cylindrical cells of widely varying aspect ratio. J. Fluid Mech. 542, 165–174.CrossRefGoogle Scholar
20. Sun, C., Xia, K.-Q. & Tong, P. 2005b Three-dimensional flow structures and dynamics of turbulent thermal convection in a cylindrical cell. Phys. Rev. E 72, 026302.CrossRefGoogle Scholar
21. Sun, C., Zhou, Q. & Xia, K.-Q. 2006 Cascades of velocity and temperature fluctuations in buoyancy-driven thermal turbulence. Phys. Rev. Lett. 97, 144504.CrossRefGoogle ScholarPubMed
22. Taylor, G. I. 1938 The spectrum of turbulence. Proc. R. Soc. Lond. A 164, 476–490.CrossRefGoogle Scholar
23. Warhaft, Z. 2000 Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32, 203–240.CrossRefGoogle Scholar
24. Xi, H.-D., Zhou, S.-Q., Zhou, Q., Chan, T.-S. & Xia, K.-Q. 2009 Origin of the temperature oscillation in turbulent thermal convection. Phys. Rev. Lett. 102, 044503.CrossRefGoogle ScholarPubMed
25. Xia, K.-Q., Sun, C. & Zhou, S.-Q. 2003 Particle image velocimetry measurement of the velocity field in turbulent thermal convection. Phys. Rev. E 68, 066303.CrossRefGoogle ScholarPubMed
26. Zhao, X. & He, G.-W. 2009 Space–time correlations of fluctuating velocities in turbulent shear flows. Phys. Rev. E 79, 046316.CrossRefGoogle ScholarPubMed
27. Zhou, Q., Sun, C. & Xia, K.-Q. 2008 Experimental investigation of homogeneity, isotropy and circulation of the velocity field in buoyancy-driven turbulence. J. Fluid Mech. 598, 361–372.CrossRefGoogle Scholar
28. Zhou, Q., Xi, H.-D., Zhou, S.-Q., Sun, C. & Xia, K.-Q. 2009 Oscillations of the large-scale circulation in turbulent Rayleigh–Bénard convection: the sloshing mode and its relationship with the torsional mode. J. Fluid Mech. 630, 367–390.CrossRefGoogle Scholar
29. Zhou, Q. & Xia, K.-Q. 2008 Comparative experimental study of local mixing of active and passive scalars in turbulent thermal convection. Phys. Rev. E 77, 056312.CrossRefGoogle ScholarPubMed
30. Zhou, Q. & Xia, K.-Q. 2010 Universality of local dissipation scales in buoyancy-driven turbulence. Phys. Rev. Lett. 104, 124301.CrossRefGoogle ScholarPubMed