Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-12T19:34:11.321Z Has data issue: false hasContentIssue false
  • English
  • Français

Effect of tilting on turbulent convection: cylindrical samples with aspect ratio $\Gamma = 0. 50$

Published online by Cambridge University Press:  09 January 2013

Stephan Weiss  and
Guenter Ahlers
Stephan Weiss
Affiliation:
Department of Physics, University of California, Santa Barbara, CA 93106, USA
Guenter Ahlers*
Affiliation:
Department of Physics, University of California, Santa Barbara, CA 93106, USA
*
†Email address for correspondence: guenter@physics.ucsb.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We report measurements of the properties of turbulent thermal convection of a fluid with a Prandtl number $\mathit{Pr}= 4. 38$ in a cylindrical cell with an aspect ratio $\Gamma = 0. 50$. The rotational symmetry was broken by a small tilt of the sample axis relative to gravity. Measurements of the heat transport (as expressed by the Nusselt number Nu), as well as properties of the large-scale circulation (LSC) obtained from temperature measurements along the sidewall, are presented. In contradistinction to similar experiments using containers of aspect ratio $\Gamma = 1. 00$ (Ahlers et al., J. Fluid Mech., vol. 557, 2006b, pp. 347–367) and $\Gamma = 0. 50$ (Chillà et al., Eur. Phys. J. B, vol. 40, 2004, pp. 223–227; Sun, Xi & Xia, Phys. Rev. Lett., vol. 95, 2005, p. 074502; Roche et al., New J. Phys., vol. 12, 2010, p. 085014), we see a very small increase of the heat transport for tilt angles up to about 0.1 rad. Based on measurements of properties of the LSC we explain this increase by a stabilization of the single-roll state (SRS) of the LSC and a destabilization of the double-roll state (DRS) (it is known from previous work that the SRS has a slightly larger heat transport than the DRS). Quantitative measurements of the strength and the orientation of the LSC show that its azimuthal diffusion is suppressed with increasing tilt whereas the torsional oscillation becomes more pronounced and its frequency increases.

JFM classification

Convection: Convection
Type
Papers
Information
Journal of Fluid Mechanics , Volume 715 , 25 January 2013 , pp. 314 - 334
Copyright
©2013 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ahlers, G. 2009 Turbulent convection. Physics 2, 74.CrossRefGoogle Scholar
Ahlers, G., Bodenschatz, E., Funfschilling, D. & Hogg, J. 2009a Turbulent Rayleigh–Bénard convection for a Prandtl number of 0.67. J. Fluid Mech. 641, 157–167.Google Scholar
Ahlers, G., Brown, E., Fontenele Araujo, F., Funfschilling, D., Grossmann, S. & Lohse, D. 2006a Non-Oberbeck–Boussinesq effects in strongly turbulent Rayleigh–Bénard convection. J. Fluid Mech. 569, 409–445.CrossRefGoogle Scholar
Ahlers, G., Brown, E. & Nikolaenko, A. 2006b The search for slow transients, and the effect of imperfect vertical alignment, in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 557, 347–367.Google Scholar
Ahlers, G., Grossmann, S. & Lohse, D. 2009b Heat transfer and large-scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81, 503–538.CrossRefGoogle Scholar
Assaf, M., Angheluta, L. & Goldenfeld, N. 2011 Rare fluctuations and large-scale circulation cessations in turbulent convection. Phys. Rev. Lett. 107, 044502.Google Scholar
Bailon-Cuba, J., Emran, M. & Schumacher, J. 2010 Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection. J. Fluid Mech. 655, 152–173.CrossRefGoogle Scholar
Boussinesq, J. 1903 Theorie analytique de la chaleur, Vol. 2. Gauthier-Villars.Google Scholar
Brown, E. & Ahlers, G. 2006a Effect of the Earth’s Coriolis force on turbulent Rayleigh–Bénard convection in the laboratory. Phys. Fluids 18, 125108.Google Scholar
Brown, E. & Ahlers, G. 2006b Rotations and cessations of the large-scale circulation in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 568, 351–386.Google Scholar
Brown, E. & Ahlers, G. 2007 Temperature gradients and search for non-Boussinesq effects in the interior of turbulent Rayleigh–Bénard convection. Europhys. Lett. 80, 14001.Google Scholar
Brown, E. & Ahlers, G. 2008a Azimuthal asymmetries of the large-scale circulation in turbulent Rayleigh–Bénard convection. Phys. Fluids 20, 105105.Google Scholar
Brown, E. & Ahlers, G. 2008b 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.Google Scholar
Brown, E. & Ahlers, G. 2009 The origin of oscillations of the large-scale circulation of turbulent Rayleigh–Bénard convection. J. Fluid Mech. 638, 383–400.CrossRefGoogle Scholar
Brown, E., Funfschilling, D. & Ahlers, G. 2007 Anomalous Reynolds-number scaling in turbulent Rayleigh–Bénard convection. J. Stat. Mech. 2007, 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.Google Scholar
Chillà, F., Rastello, M., Chaumat, S. & Castaing, B. 2004 Long relaxation times and tilt sensitivity in Rayleigh–Bénard turbulence. Eur. Phys. J. B 40, 223–227.Google Scholar
Ciliberto, S., Cioni, S. & Laroche, C. 1996 Large-scale flow properties of turbulent thermal convection. Phys. Rev. E 54, R5901–R5904.Google Scholar
Cioni, S., Ciliberto, S. & Sommeria, J. 1996 Experimental study of high Rayleigh-number convection in mercury and water. Dyn. Atmos. Oceans 24, 117–127.CrossRefGoogle Scholar
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.Google 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
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.Google Scholar
Grossmann, S. & Lohse, D. 2001 Thermal convection for large Prandtl number. Phys. Rev. Lett. 86, 3316–3319.CrossRefGoogle Scholar
Howard, R. & LaBonte, B. 1980 The sun is observed to be a torsional oscillator with a period of 11 years. Astrophys. J. 239, L33–L36.Google Scholar
Kadanoff, L. P. 2001 Turbulent heat flow: structures and scaling. Phys. Today 54 (8), 34–39.Google Scholar
Kühn, M., Bosbach, J. & Wagner, C. 2009 Experimental parametric study of forced and mixed convection in a passenger aircraft cabin mock-up. Build Environ. 44 (5), 961–970.CrossRefGoogle Scholar
Lohse, D. & Xia, K.-Q. 2010 Small-scale properties of turbulent Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 42, 335–364.Google Scholar
Oberbeck, A. 1879 über die Wärmeleitung der Flüssigkeiten bei Berücksichtigung der Strömungen infolge von Temperaturdifferenzen. Ann. Phys. Chem. 7, 271.Google Scholar
van der Poel, E. P., Stevens, R. & Lohse, D. 2011 Connecting flow structures and heat flux in turbulent Rayleigh–Bénard convection. Phys. Rev. E 84, 045303(R).Google Scholar
Qiu, X. L. & Tong, P. 2002 Temperature oscillations in turbulent Rayleigh–Bénard convection. Phys. Rev. E 66, 026308.CrossRefGoogle ScholarPubMed
Rahmstorf, S. 2000 The thermohaline ocean circulation: a system with dangerous thresholds? Climate Change 46, 247–256.CrossRefGoogle Scholar
Roche, P.-E., Castaing, B., Chabaud, B. & Hébral, B. 2002 Prandtl and Rayleigh numbers dependences in Rayleigh–Bénard convection. Europhys. Lett. 58 (5), 693.CrossRefGoogle Scholar
Roche, P.-E., Gauthier, F., Kaiser, R. & Salort, J. 2010 On the triggering of the Ultimate Regime of convection. New J. Phys. 12, 085014.Google Scholar
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.Google Scholar
Stacey, W. M. 2010 Fusion: An Introduction to the Physics and Technology of Magnetic Confinement Fusion. Wiley.Google Scholar
Stevens, R. J., Clercx, H. J. & Lohse, D. 2011 Effect of plumes on measuring the large-scale circulation. Phys. Fluids 23, 095110.Google Scholar
Sun, C., Xi, H. D. & Xia, K. Q. 2005 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.Google Scholar
Verzicco, R. & Camussi, R. 2003 Numerical experiments on strongly turbulent thermal convection in a slender cylindrical cell. J. Fluid Mech. 477, 19–49.Google Scholar
Weiss, S. & Ahlers, G. 2011a Heat transport by turbulent rotating Rayleigh–Bénard convection and its dependence on the aspect ratio. J. Fluid Mech. 684, 407–426.Google Scholar
Weiss, S. & Ahlers, G. 2011b Turbulent Rayleigh–Bénard convection in a cylindrical container with aspect ratio $\gamma = 0. 50$ and Prandtl number $Pr= 4. 38$. J. Fluid Mech. 676, 1–4.Google 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. & Xia, K.-Q. 2008a Azimuthal motion, reorientation, cessation, and reversals of the large-scale circulation in turbulent thermal convection: a comparative study in aspect ratio oner and one-half geometries. Phys. Rev. E 78, 036326.CrossRefGoogle Scholar
Xi, H.-D. & Xia, K.-Q. 2008b Flow mode transition in turbulent thermal convection. Phys. Fluids 20, 055104.CrossRefGoogle Scholar
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.Google Scholar
Zhong, J.-Q. & Ahlers, G. 2010 Heat transport and the large-scale circulation in rotating turbulent Rayleigh–Bénard convection. J. Fluid Mech. 665, 300–333.Google Scholar