Skip to main content Accessibility help
×
Home

The origin of oscillations of the large-scale circulation of turbulent Rayleigh–Bénard convection

  • ERIC BROWN (a1) and GUENTER AHLERS (a2)

Abstract

In agreement with a recent experimental discovery by Xi et al. (Phys. Rev. Lett., vol. 102, 2009, paper no. 044503), we also find a sloshing mode in experiments on the large-scale circulation (LSC) of turbulent Rayleigh–Bénard convection in a cylindrical sample of aspect ratio one. The sloshing mode has the same frequency as the torsional oscillation discovered by Funfschilling & Ahlers (Phys. Rev. Lett., vol. 92, 2004, paper no. 1945022004). We show that both modes can be described by an extension of a model developed previously Brown & Ahlers (Phys. Fluids, vol. 20, 2008, pp. 105105-1–105105-15; Phys. Fluids, vol. 20, 2008, pp. 075101-1–075101-16). The extension consists of permitting a lateral displacement of the LSC circulation plane away from the vertical centreline of the sample as well as a variation of the displacement with height (such displacements had been excluded in the original model). Pressure gradients produced by the sidewall of the container on average centre the plane of the LSC so that it prefers to reach its longest diameter. If the LSC is displaced away from this diameter, the walls provide a restoring force. Turbulent fluctuations drive the LSC away from the central alignment, and combined with the restoring force they lead to oscillations. These oscillations are advected along with the LSC. This model yields the correct wavenumber and phase of the oscillations, as well as estimates of the frequency, amplitude and probability distributions of the displacements.

Copyright

Corresponding author

Email address for correspondence: guenter@physics.uscb.edu

References

Hide All
Ahlers, G., Brown, E. & Nikolaenko, A. 2006 The search for slow transients, and the effect of imperfect vertical alignment, in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 557, 347367.
Ahlers, G., Grossmann, S. & Lohse, D. 2009 Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81, 503537.
Brown, E. & Ahlers, G. 2006 a Effect of the Earth's Coriolis force on turbulent Rayleigh–Bénard convection in the laboratory. Phys. Fluids 18, 125108-1–125108-15.
Brown, E. & Ahlers, G. 2006 b Rotations and cessations of the large-scale circulation in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 568, 351386.
Brown, E. & Ahlers, G. 2007 a Large-scale circulation model of turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 98, 134501-1–134501-4.
Brown, E. & Ahlers, G. 2007 b Temperature gradients and search for non-Boussinesq effects in the interior of turbulent Rayleigh–Bénard convection. Europhys. Lett. 80, 14001-1–14001-6.
Brown, E. & Ahlers, G. 2008 a Azimuthal asymmetries of the large-scale circulation in turbulent Rayleigh–Bénard convection. Phys. Fluids 20, 105105-1–105105-15.
Brown, E. & Ahlers, G. 2008 b A model of diffusion in a potential well for the dynamics of the large-scale circulation in turbulent Rayleigh–Bénard convection. Phys. Fluids 20, 075101-1–075101-16.
Brown, E., Funfschilling, D. & Ahlers, G. 2007 Anomalous Reynolds-number scaling in turbulent Rayleigh–Bénard convection. J. Stat. Mech. 2007, P10005-1–P10005-22.
Brown, E., Nikolaenko, A. & Ahlers, G. 2005 Reorientation of the large-scale circulation in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 95, 084503.
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, 130.
Ciliberto, S., Cioni, S. & Laroche, C. 1996 Large-scale flow properties of turbulent thermal convection. Phys. Rev. E 54, R5901R5904.
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, 111140.
Funfschilling, D. & Ahlers, G. 2004 Plume motion and large scale circulation in a cylindrical Rayleigh–Bénard cell. Phys. Rev. Lett. 92, 194502.
Funfschilling, D., Brown, E. & Ahlers, G. 2008 Torsional oscillations of the large-scale circulation in turbulent Rayleigh–Bénard convection. J. Fluid Mech 607, 119139.
Gitterman, M. 2005 The Noisy Oscillator: The First Hundred Years, from Einstein Until Now. World Scientific.
Heslot, F., Castaing, B. & Libchaber, A. 1987 Transition to turbulence in helium gas. Phys. Rev. A 36, 58705873.
Niemela, J. J., Skrbek, L., Sreenivasan, K. R. & Donnelly, R. J. 2001 The wind in confined thermal turbulence. J. Fluid Mech. 449, 169178.
Qiu, X. L., Shang, X. D., Tong, P. & Xia, K.-Q. 2004 Velocity oscillations in turbulent Rayleigh–Bénard convection. Phys. Fluids. 16, 412423.
Qiu, X. L. & Tong, P. 2000 Large-scale coherent rotation and oscillation in turbulent thermal convection. Phys. Rev. E 61, R6075R6078.
Qiu, X. L. & Tong, P. 2001 a Large scale velocity structures in turbulent thermal convection. Phys. Rev. E 64, 036304-1–036304-13.
Qiu, X. L. & Tong, P. 2001 b Onset of coherent oscillations in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett 87, 094501-1–094501-4.
Qiu, X. L. & Tong, P. 2002 Temperature oscillations in turbulent Rayleigh–Bénard convection. Phys. Rev. E 66, 026308-1–026308-12.
Resagk 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, 095105-1–095105-15.
Sano, M., Wu, X. Z. & Libchaber, A. 1989 Turbulence in helium-gas free convection. Phys. Rev. A 40, 64216430.
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.
Sun, C. & Xia, K.-Q. 2005 Scaling of the Reynolds number in turbulent thermal convection. Phys. Rev. E 72, 067302-1–067302-4.
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, 026302-1–026302-13.
Takeshita, T., Segawa, T., Glazier, J. A. & Sano, M. 1996 Thermal turbulence in mercury. Phys. Rev. Lett. 76, 14651468.
Tsuji, Y., Mizuno, T., Mashiko, T. & Sano, M. 2005 Mean wind in convective turbulence of mercury. Phys. Rev. Lett. 94, 034501.
Villermaux, E. 1995 Memory-induced low frequency oscillations in closed convection boxes. Phys. Rev. Lett. 75, 46184621.
Xi, H. D., Zhou, Q. & Xia, K. Q. 2006 Azimuthal motion of the mean wind in turbulent thermal convestion. Phys. Rev. E 73, 056312-1–056312-13.
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.
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, 367390.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

The origin of oscillations of the large-scale circulation of turbulent Rayleigh–Bénard convection

  • ERIC BROWN (a1) and GUENTER AHLERS (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed