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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

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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