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Oscillations of the large-scale circulation in turbulent Rayleigh–Bénard convection: the sloshing mode and its relationship with the torsional mode

Published online by Cambridge University Press:  10 July 2009

QUAN ZHOU ,
HENG-DONG XI ,
SHENG-QI ZHOU ,
CHAO SUN  and
KE-QING XIA
QUAN ZHOU
Affiliation:
Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, China
HENG-DONG XI
Affiliation:
Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, China
SHENG-QI ZHOU
Affiliation:
Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, China
CHAO SUN
Affiliation:
Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, China
KE-QING XIA*
Affiliation:
Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, China
*
Email address for correspondence: kxia@phy.cuhk.edu.hk
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Abstract

We report an experimental study of the large-scale circulation (LSC) in a turbulent Rayleigh–Bénard convection cell with aspect ratio unity. The temperature-extrema-extraction (TEE) method for obtaining the dynamic information of the LSC is presented. With this method, the azimuthal angular positions of the hot ascending and cold descending flows along the sidewall are identified from the measured instantaneous azimuthal temperature profile. The motion of the LSC is then decomposed into two different modes based on these two angles: the azimuthal mode and the translational or sloshing mode that is perpendicular to the vertical circulation plane of the LSC. Comparing to the previous sinusoidal-fitting (SF) method, it is found that both the TEE and the SF methods give the same information about the azimuthal motion of the LSC, but the TEE method in addition can provide information about the sloshing motion of the LSC. The sloshing motion is found to oscillate time-periodically around the cell's central vertical axis with an amplitude being nearly independent of the turbulent intensity and to have a π/2 phase difference with the torsional mode. It is further found that the azimuthal angular positions of the hot ascending and cold descending flows oscillate out of phase with each other by π, which leads to the observations of the torsional mode when these two flows are near the top and the bottom plates, respectively, and of the sloshing mode when they are both near the mid-height plane. A direct velocity measurement further confirms the existence of the bulk sloshing mode of the flow field.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 630 , 10 July 2009 , pp. 367 - 390
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Ahlers, G., Grossmann, S. & Lohse, D. In press Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys.Google Scholar
Ashkenazi, S. & Steinberg, V. 1999 High Rayleigh number turbulent convection in a gas near the gas–liquid critical point. Phys. Rev. Lett. 83, 3641–3644.CrossRefGoogle Scholar
Brown, E. & Ahlers, G. 2006 Rotations and cessations of the large-scale circulation in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 568, 351–386.CrossRefGoogle Scholar
Brown, E., Funfschilling, D. & Ahlers, G. 2007 Anomalous Reynolds-number scaling in turbulent Rayleigh–Bénard convection. J. Stat. Mech. P10005.CrossRefGoogle Scholar
Brown, E., Nikolaenko, A. & Ahlers, G. 2005 Reorientation of the large-scale circulation in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 95, 084503.CrossRefGoogle ScholarPubMed
Burr, U., Kinzelbach, W. & Tsinober, A. 2003 Is the turbulent wind in convective flows driven by fluctuations? Phys. Fluids 15, 2313–2320.CrossRefGoogle Scholar
Castaing, B., Gunaratne, G., Heslot, F., Kadanoff, L., Libchaber, A., Thomae, S., Wu, X.-Z., Zaleski, S. & Zanetti, G. 1989 Scaling of hard thermal turbulence in Rayleigh–Bénard convection. J. Fluid Mech. 204, 1–30.CrossRefGoogle Scholar
Ciliberto, S., Cioni, S. & Laroche, C. 1996 Large-scale flow properties of turbulent thermal convection. Phys. Rev. E 54, R5901–R5904.Google ScholarPubMed
Cioni, S., Ciliberto, S. & Sommeria, J. 1997 Strongly turbulent Rayleign–Bénard convection in mercury: comparison with results at moderate Prandtl number. J. Fluid Mech. 335, 111–140.CrossRefGoogle Scholar
Funfschilling, D. & Ahlers, G. 2004 Plume motion and large-scale circulation in a cylindrical Rayleigh-Benard cell. Phys. Rev. Lett. 92, 194502.CrossRefGoogle Scholar
Funfschilling, D., Brown, E. & Ahlers, G. 2008 Torsional oscillations of the large-scale circulation in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 607, 119–139.CrossRefGoogle Scholar
Heslot, F., Castaing, B. & Libchaber, A. 1987 Transitions to turbulence in helium gas. Phys. Rev. A 36, 5870–5873.CrossRefGoogle ScholarPubMed
Krishnamurti, R. & Howard, L. N. 1981 Large-scale flow generation in turbulent convection. Proc. Natl. Acad. Sci. USA 78, 1981–1985.CrossRefGoogle ScholarPubMed
Lam, S., Shang, X.-D., Zhou, S.-Q. & Xia, K.-Q. 2002 Prandtl number dependence of the viscous boundary layer and the Reynolds numbers in Rayleigh–Bénard convection. Phys. Rev. E 65, 066306.Google ScholarPubMed
Mashiko, T., Tsuji, Y., Mizuno, T. & Sano, M. 2004 Instantaneous measurement of velocity fields in developed thermal turbulence in mercury. Phys. Rev. E 69, 036306.Google ScholarPubMed
Niemela, J. J., Skrbek, L., Sreenivasan, K. R. & Donnelly, R. J. 2001 The wind in confined thermal convection. J. Fluid Mech. 449, 169–178.CrossRefGoogle Scholar
Niemela, J. J. & Sreenivasan, K. R. 2006 Turbulent convection at high Rayleigh numbers and aspect ratio 4. J. Fluid Mech. 557, 411–422.CrossRefGoogle Scholar
du Puits, R., Resagk, C. & Thess, A. 2007 Breakdown of wind in turbulent thermal convection. Phys. Rev. E 75, 016302.Google ScholarPubMed
Qiu, X.-L., Shang, X.-D., Tong, P. & Xia, K.-Q. 2004 Velocity oscillations in turbulent Rayleigh–Bénard convection. Phys. Fluid 16, 412–423.CrossRefGoogle Scholar
Qiu, X.-L. & Tong, P. 2001 a Onset of coherent oscillations in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 87, 094501.CrossRefGoogle ScholarPubMed
Qiu, X.-L. & Tong, P. 2001 b Large-scale velocity structures in turbulent thermal convection. Phys. Rev. E 64, 036304.Google ScholarPubMed
Qiu, X.-L. & Tong, P. 2002 Temperature oscillations in turbulent Rayleigh–Bénard convection. Phys. Rev. E 66, 026308.Google ScholarPubMed
Qiu, X.-L., Yao, Y.-S. & Tong, P. 2000 Large-scale coherent rotation and oscillation in turbulent thermal convection. Phys. Rev. E 61, R6075–6078.Google ScholarPubMed
Rehab, H., Villermaux, E. & Hopfinger, E. J. 1997 Flow regimes of large-velocity-ratio coaxial jets. J. Fluid Mech. 345, 357–381.CrossRefGoogle Scholar
Resagk, C., du Puits, R., Thess, A., Dolzhansky, F. V., Grossmann, S., Fontenele Araujo, F. & Lohse, D. 2006 Oscillations of the large scale wind in turbulent thermal convection. Phys. Fluids 18, 095105.CrossRefGoogle Scholar
Sano, M., Wu, X.-Z. & Libchaber, A. 1989 Turbulence in helium-gas free convection. Phys. Rev. A 40, 6421–6430.CrossRefGoogle ScholarPubMed
Shang, X.-D. & Xia, K.-Q. 2001 Scaling of the velocity power spectra in turbulent thermal convection. Phys. Rev. E 64, 065301 (R).Google ScholarPubMed
Siggia, E. D. 1994 High Rayleigh number convection. Annu. Rev. Fluid. Mech. 26, 137–168.CrossRefGoogle Scholar
Sreenivasan, K. R., Bershadskii, A. & Niemela, J. J. 2002 Mean wind and its reversal in thermal convection. Phys. Rev. E 65, 056306.Google ScholarPubMed
Sun, C., Xi, H.-D. & Xia, K.-Q. 2005 a Azimuthal symmetry, flow dynamics, and heat transport in turbulent thermal convection in a cylinder with an aspect ratio of 0.5. Phys. Rev. Lett. 95, 074502.CrossRefGoogle Scholar
Sun, C. & Xia, K.-Q. 2005 Scaling of the Reynolds number in turbulent thermal convection. Phys. Rev. E 72, 067302.Google ScholarPubMed
Sun, C. & Xia, K.-Q. 2007 Multi-point local temperature measurements inside the conducting plates in turbulent thermal convection. J. Fluid Mech. 570, 479–489.CrossRefGoogle Scholar
Sun, C., Xia, K.-Q. & Tong, P. 2005 b Three-dimensional flow structures and dynamics of turbulent thermal convection in a cylindrical cell. Phys. Rev. E 72, 026302.Google Scholar
Takeshita, T., Segawa, T., Glazier, J. A. & Sano, M. 1996 Thermal turbulence in mercury. Phys. Rev. E 76, 1465–1468.Google ScholarPubMed
Tilgner, A., Belmonte, A. & Libchaber, A. 1993 Temperature and velocity profiles of turbulent convection in water. Phys. Rev. E 47, R2253–R2256.Google ScholarPubMed
Tsuji, Y., Mizuno, T., Mashiko, T. & Sano, M. 2005 Mean wind in convective turbulence of mercury. Phys. Rev. Lett. 94, 034501.CrossRefGoogle ScholarPubMed
Villermaux, E. 1995 Memory-induced low frequency oscillations in closed convection boxes. Phys. Rev. Lett. 75, 4618–4621.CrossRefGoogle ScholarPubMed
Xi, H.-D., Lam, S. & Xia, K.-Q. 2004 From laminar plumes to organized flows: the onset of large-scale circulation in turbulent thermal convection. J. Fluid Mech. 503, 47–56.CrossRefGoogle Scholar
Xi, H.-D. & Xia, K.-Q. 2007 Cessations and reversals of the large-scale circulation in turbulent thermal convection. Phys. Rev. E 75, 066307.Google ScholarPubMed
Xi, H.-D. & Xia, K.-Q. 2008 a Flow mode transitions in turbulent thermal convection. Phys. Fluids 20, 055104.CrossRefGoogle Scholar
Xi, H.-D. & Xia, K.-Q. 2008 b Azimuthal motion, reorientation, cessation, and reversal of the large-scale circulation in turbulent thermal convection: a comparative study in aspect ratio one and one-half geometries. Phys. Rev. E 78, 036326.Google ScholarPubMed
Xi, H.-D., Zhou, Q. & Xia, K.-Q. 2006 Azimuthal motion of the mean wind in turbulent thermal convection. Phys. Rev. E 73, 056312.Google ScholarPubMed
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
Xia, K.-Q. 2007 Two clocks for a single engine in turbulent convection. J. Stat. Mech. N11001.CrossRefGoogle Scholar
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.Google ScholarPubMed
Zhou, Q., Sun, C. & Xia, K.-Q. 2007 a Morphological evolution of thermal plumes in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 98, 074501.CrossRefGoogle ScholarPubMed
Zhou, S.-Q., Sun, C. & Xia, K.-Q. 2007 bMeasured oscillations of the velocity and temperature fields in turbulent Rayleigh–Bénard convection in a rectangular cell. Phys. Rev. E 76, 036301.Google Scholar