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Torsional oscillations of the large-scale circulation in turbulent Rayleigh–Bénard convection

Published online by Cambridge University Press:  30 June 2008

DENIS FUNFSCHILLING ,
ERIC BROWN  and
GUENTER AHLERS
DENIS FUNFSCHILLING
Affiliation:
Department of Physics and iQCD, University of California, Santa Barbara, CA 93106, USA
ERIC BROWN
Affiliation:
Department of Physics and iQCD, University of California, Santa Barbara, CA 93106, USA
GUENTER AHLERS
Affiliation:
Department of Physics and iQCD, University of California, Santa Barbara, CA 93106, USA
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Abstract

Measurements over the Rayleigh-number range 108 ≲ R ≲ 1011 and Prandtl-number range 4.4≲σ≲29 that determine the torsional nature and amplitude of the oscillatory mode of the large-scale circulation (LSC) of turbulent Rayleigh–Bénard convection are presented. For cylindrical samples of aspect ratio Γ=1 the mode consists of an azimuthal twist of the near-vertical LSC circulation plane, with the top and bottom halves of the plane oscillating out of phase by half a cycle. The data for Γ=1 and σ=4.4 showed that the oscillation amplitude varied irregularly in time, yielding a Gaussian probability distribution centred at zero for the displacement angle. This result can be described well by the equation of motion of a stochastically driven damped harmonic oscillator. It suggests that the existence of the oscillations is a consequence of the stochastic driving by the small-scale turbulent background fluctuations of the system, rather than a consequence of a Hopf bifurcation of the deterministic system. The power spectrum of the LSC orientation had a peak at finite frequency with a quality factor Q≃5, nearly independent of R. For samples with Γ≥2 we did not find this mode, but there remained a characteristic periodic signal that was detectable in the area density ρp of the plumes above the bottom-plate centre. Measurements of ρp revealed a strong dependence on the Rayleigh number R, and on the aspect ratio Γ that could be represented by ρp ~ Γ2.7±0.3. Movies are available with the online version of the paper.

JFM classification

Turbulent Flows: Turbulent convection
Type
Papers
Information
Journal of Fluid Mechanics , Volume 607 , 25 July 2008 , pp. 119 - 139
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Ahlers, G., Brown, E., Fontenele Araujo, F., Funfschilling, D., Grossmann, S. & Lohse, D. 2006 Non-Oberbeck-Boussinesq effects in strongly turbulent Rayleigh-Bénard convection. J. Fluid Mech. 569, 409–445.CrossRefGoogle Scholar
Ahlers, G., Brown, E. & Nikolaenko, A. 2005 Search for slow transients, and the effect of imperfect vertical alignment, in turbulent Rayleigh-Bénard convection. J. Fluid Mech. 557, 347–367.CrossRefGoogle Scholar
Ahlers, G., Fontenele Araujo, F., Funfschilling, D., Grossmann, S. & Lohse, D. 2007 Non-Oberbeck-Boussinesq effects in gaseous Rayleigh-Bénard convection. Phys. Rev. Lett. 98, 054501.CrossRefGoogle ScholarPubMed
Ahlers, G., Grossmann, S. & Lohse, D. 2002 Hochpräzision im Kochtopf: Neues zur turbulenten Konvektion. Physik J. 1 (2), 31–37.Google Scholar
Brown, E. & Ahlers, G. 2006 a Effect of the Earth's Coriolis force on turbulent Rayleigh-Bénard convection in the laboratory. Phys. Fluids 18, 125108.CrossRefGoogle Scholar
Brown, E. & Ahlers, G. 2006 b Rotations and cessations of the large-scale circulation in turbulent Rayleigh-Bénard convection. J. Fluid Mech. 568, 351–386.CrossRefGoogle Scholar
Brown, E. & Ahlers, G. 2007 Large-scale circulation model of turbulent Rayleigh-Bénard convection. Phys. Rev. Lett. 98, 134501.CrossRefGoogle ScholarPubMed
Brown, E. & Ahlers, G. 2008 A model of diffusion in a potential well for the dynamics of the large-scale circulation in turbulent Rayleigh-Bénard convection Phys. Fluids (in press).CrossRefGoogle Scholar
Brown, E., Funfschilling, D. & Ahlers, G. 2007 Anomalous Reynolds-number scaling in turbulent Rayleigh-Bénard convection. J. Statist. Mech. P10005.CrossRefGoogle Scholar
Brown, E., Nikolaenko, A. & Ahlers, G. 2005 a Reorientation of the large-scale circulation in turbulent Rayleigh-Bénard convection. Phys. Rev. Lett 95, 084503.CrossRefGoogle ScholarPubMed
Brown, E., Nikolaenko, A., Funfschilling, D. & Ahlers, G. 2005 b Heat transport in turbulent Rayleigh-Bénard convection: Effect of finite top- and bottom-plate conductivities. Phys. Fluids 17, 075108.CrossRefGoogle Scholar
de Bruyn, J. R., Bodenschatz, E., Morris, S. W., Trainoff, S., Hu, Y., Cannell, D. S. & Ahlers, G. 1996 Apparatus for the study of Rayleigh-Bénard convection in gases under pressure. Rev. Sci. Instrum. 67, 2043–2067.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 Rayleigh-Bénard convection in mercury: comparison with results at moderate Prandtl number. J. Fluid Mech. 335, 111–140.CrossRefGoogle Scholar
van Doorn, E., Dhruva, B., Sreenivasan, K. R. & Cassella, V. 2000 Statistics of wind direction and its increments. Phys. Fluids 12, 1529–1534.CrossRefGoogle Scholar
Du, Y. B. & Tong, P. 1998 Enhanced heat transport in turbulent convection over a rough surface. Phys. Rev. Lett. 81, 987–990.CrossRefGoogle Scholar
Funfschilling, D. & Ahlers, G. 2004 Plume motion and large scale circulation in a cylindrical Rayleigh-Bénard cell. Phys. Rev. Lett. 92, 194502.CrossRefGoogle Scholar
Gitterman, M. 2005 The Noisy Oscillator, The First Hundred Years, From Einstein Until Now. World Scientific.CrossRefGoogle Scholar
Glatzmaier, G., R. Coe, L. H. & Roberts, P. 1999 The role of the Earth's mantle in controlling the frequency of geomagnetic reversals. Nature 401, 885–890.CrossRefGoogle Scholar
Gluckman, B. J., Willaime, H. & Gollub, J. 1993 Geometry of isothermal and isoconcentration surfaces in thermal turbulence. Phys. Fluids A 5, 646–761.CrossRefGoogle Scholar
Haramina, T. & Tilgner, A. 2004 Coherent structures in boundary layers of rayleigh-bnard convection. Phys. Rev. E 69, 056306.Google ScholarPubMed
Heslot, F., Castaing, B. & Libchaber, A. 1987 Transition to turbulence in helium gas. Phys. Rev. A 36, 5870–5873.CrossRefGoogle ScholarPubMed
Kadanoff, L. P. 2001 Turbulent heat flow: Structures and scaling. Phys. Today 54 (8), 34–39.CrossRefGoogle Scholar
Kelly, R. E. 1994 The onset and development of thermal convection in fully developed shear flow. Adv. Appl. Mech 31, 31–512.Google Scholar
Moses, E., Zocchi, G. & Libchaber, A. 1993 An experimental study of laminar plumes. J. Fluid Mech. 251, 586–101.CrossRefGoogle Scholar
Moses, E., Zocchi, G., Procaccia, I. & Libchaber, A. 1991 The dynamics and interaction of laminar thermal plumes. Europhys. Lett. 14, 56–50.CrossRefGoogle Scholar
Niemela, J., Skrbek, L., Sreenivasan, K. R. & Donnelly, R. J. 2001 The wind in confined thermal turbulence. J. Fluid Mech. 449, 169–178.CrossRefGoogle Scholar
Puthenveettil, B. A. & Arakeri, J. H. 2005 Plume structure in high-rayleigh-number convection. J. Fluid Mech. 542, 212–749.CrossRefGoogle Scholar
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
Qiu, X. L. & Tong, P. 2001 a Large scale velocity structures in turbulent thermal convection. Phys. Rev. E 64, 036304.Google ScholarPubMed
Qiu, X. L. & Tong, P. 2001 b Onset of coherent oscillations in turbulent Rayleigh-Bénard convection. Phys. Rev. Lett 87, 094501.CrossRefGoogle 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, S. H. & Tong, P. 2000 Large-scale coherent rotation and oscillation in turbulent thermal convection. Phys. Rev. E 61, R6075.Google ScholarPubMed
Rasenat, S., Hartung, G., Winkler, B. I. & Rehberg, I. 1989 The shadowgraph method in convection experiments. Exps. Fluids 7, 412–420.CrossRefGoogle Scholar
Resagk, C., du Puits, R., Thess, A., Dolzhansky, F., 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, 6426–1430.CrossRefGoogle ScholarPubMed
Shang, X. D., Qiu, X. L., Tong, P. & Xia, K.-Q. 2003 Measured local heat transport in turbulent Rayleigh-Bénard convection. Phys. Rev. Lett. 90, 074501.CrossRefGoogle ScholarPubMed
Siggia, E. D. 1994 High Rayleigh number convection. Annu. Rev. Fluid Mech. 26, 137–168.CrossRefGoogle Scholar
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. & 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. Lett. 76, 1465–1468.CrossRefGoogle ScholarPubMed
Tanaka, H. & Miyata, H. 1980 Turbulent natural convection in a horizontal water layer heated from below. Intl J. Heat Mass Transfer 23, 1273–1281.Google Scholar
Trainoff, S. P. & Cannell, D. S. 2002 Physical optics treatment of the shadowgraph. Rev. Sci. Instrum. 14, 1341–0363.Google Scholar
Tsuji, Y., Mizuno, T., Mashiko, T. & Sano, M. 2005 Mean wind in convective turbulence of mercury. Phys. Rev. Lett. 94, 034501.CrossRefGoogle ScholarPubMed
Verzicco, R. 2002 Sidewall finite conductivity effects in confined turbulent thermal convection. J. Fluid Mech. 473, 201–210.CrossRefGoogle Scholar
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., Zhou, Q. & Xia, K. Q. 2006 Azimuthal motion of the mean wind in turbulent thermal convestion. Phys. Rev. E 73, 056312.Google Scholar
Xu, X., Bajaj, K. M. S. & Ahlers, G. 2000 Heat transport in turbulent Rayleigh-Bénard convection. Phys. Rev. Lett. 84, 4357–4360.CrossRefGoogle ScholarPubMed
Zhang, J., Childress, S. & Libchaber, A. 1997 Non-Boussinesq effect: Thermal convection with broken symmetry. Phys. Fluids 9, 1034–1042.CrossRefGoogle Scholar
Zhou, S. Q., Sun, C. & Xia, K. Q. 2007 Measured oscillations of the velocity and temperature fields in turbulent Rayleigh-Bénard convection in a rectangular cell. Phys. Rev. E 76, 036301.Google Scholar
Zocchi, G., Moses, E. & Libchaber, A. 1990 Coherent structures in turbulent convection: an experimental study. Physica A 166, 387–407.CrossRefGoogle Scholar

Funfschilling et al. supplementary movie

Movie 1. Shadowgraph movie for the small aspect-ratio-one sample, in a cylinder of diameter 8.66 cm and height 8.74 cm, heated from below with methanol as the fluid. The view is from the top along the axis of the cylinder. The dark elongated stripes are warm plumes near the bottom plate, and the bright stripes are cold plumes near the top plate. Their motion, on average in opposite directions, reflects the motion of the large-scale circulation near the bottom and top plates. The mean temperature was 40 deg. C and Rayleigh number R = 1.2 X 10^8. The movie corresponds to the image shown in figure 14(b). When displayed at 30 frames/sec, it runs at 7.6 times real speed.

Download Funfschilling et al. supplementary movie(Video)
Video 4.9 MB

Funfschilling et al. supplementary movie

Movie 2. Shadowgraph movie for the small aspect-ratio-one sample with methanol at a mean temperature of 40 deg. C and R = 4.6 X 10^8 corresponding to figure 14(d). When displayed at 30 frames/sec, the movie runs at 7.6 times real speed.

Download Funfschilling et al. supplementary movie(Video)
Video 4.9 MB