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Mean flow structure in horizontal convection

Published online by Cambridge University Press:  05 January 2017

Olga Shishkina Open the ORCID record for Olga Shishkina [Opens in a new window]
Olga Shishkina*
Affiliation:
Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, D-37077 Göttingen, Germany
*
†Email address for correspondence: [email protected]
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Abstract

We analyse the global flow structures in horizontal convection systems, where the heat supply and removal takes place through separated parts of a lower horizontal surface of a fluid layer. The results are based on direct numerical simulations for the length-to-height aspect ratio of the convection cell $\unicode[STIX]{x1D6E4}=10$, Rayleigh number $\mathit{Ra}$ from $3\times 10^{8}$ to $3\times 10^{11}$ and Prandtl number $\mathit{Pr}$ from 0.05 to 50. The structure of the mean flows in horizontal convection is described in terms of time-averaged spatial distributions of the temperature, velocity, kinetic energy, thermal and kinetic dissipation rates. A possible scenario of transition to turbulent horizontal convection in the whole convection cell of a large aspect ratio is discussed.

JFM classification

Convection: Convection
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Papers
Information
Journal of Fluid Mechanics , Volume 812 , 10 February 2017 , pp. 525 - 540
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Copyright
© 2017 Cambridge University Press 

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References

Ahlers, G., Grossmann, S. & Lohse, D. 2009 Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81, 503–537.Google Scholar
Bodenschatz, E., Pesch, W. & Ahlers, G. 2000 Recent developments in Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 32, 709–778.Google Scholar
Boffetta, G. & Ecke, R. E. 2012 Two-dimensional turbulence. Annu. Rev. Fluid Mech. 44, 427–451.Google Scholar
Chillà, F. & Schumacher, J. 2012 New perspectives in turbulent Rayleigh–Bénard convection. Eur. Phys. J. E 35, 58.Google ScholarPubMed
Chiu-Webster, S., Hinch, E. J. & Liter, J. R. 2008 Very viscous horizontal convection. J. Fluid Mech. 611, 395–426.CrossRefGoogle Scholar
Cushman-Roisin, B. & Beckers, J.-M. 2011 Introduction to Geophysical Fluid Dynamics. Physical and Numerical Aspects, 2nd edn. Academic.Google Scholar
Daya, Z. A. & Ecke, R. E. 2001 Does turbulent convection feel the shape of the container? Phys. Rev. Lett. 87, 184501.Google Scholar
Gayen, B., Griffiths, R. W. & Hughes, G. O. 2014 Stability transitions and turbulence in horizontal convection. J. Fluid Mech. 751, 698–724.CrossRefGoogle Scholar
Gibert, M., Pabiou, H., Chillà, F. & Castaing, B. 2006 High-Rayleigh-number convection in a vertical channel. Phys. Rev. Lett. 96, 084501.Google Scholar
Gramberg, H. J. J., Howell, P. D. & Ockendon, J. R. 2007 Convection by a horizontal thermal gradient. J. Fluid Mech. 586, 41–57.Google Scholar
Griffiths, R. W., Hughes, G. O. & Gayen, B. 2013 Horizontal convection dynamics: insights from transient adjustment. J. Fluid Mech. 726, 559–595.Google Scholar
Griffiths, R. W., Maher, N. & Hughes, G. O. 2011 Horizontal convection under oscillatory buoyancy forcing. J. Mar. Res. 69, 523–543.Google Scholar
Grossmann, S. & Lohse, D. 2000 Scaling in thermal convection: a unifying theory. J. Fluid Mech. 407, 27–56.CrossRefGoogle Scholar
Grossmann, S. & Lohse, D. 2001 Thermal convection for large Prandtl numbers. Phys. Rev. Lett. 86, 3316–3319.Google Scholar
Hanasoge, S., Gizon, L. & Sreenivasan, K. R. 2016 Seismic sounding of convection in the sun. Annu. Rev. Fluid Mech. 48, 191–217.CrossRefGoogle Scholar
Hassanzadeh, P., Chini, G. P. & Doering, C. R. 2014 Wall to wall optimal transport. J. Fluid Mech. 751, 627–662.Google Scholar
He, X., Funfschilling, D., Nobach, H., Bodenschatz, E. & Ahlers, G. 2012 Transition to the ultimate state of turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 108, 024502.Google Scholar
Horn, S. & Shishkina, O. 2015 Toroidal and poloidal energy in rotating Rayleigh–Bénard convection. J. Fluid Mech. 762, 232–255.Google Scholar
Houghton, J. T. 1977 The Physics of Atmospheres. Cambridge University Press.Google Scholar
Huang, S.-D., Wang, F., Xi, H.-D. & Xia, K.-Q. 2015 Comparative experimental study of fixed temperature and fixed heat flux boundary conditions in turbulent thermal convection. Phys. Rev. Lett. 115, 154502.Google Scholar
Hughes, G. O. & Griffiths, R. W. 2008 Horizontal convection. Annu. Rev. Fluid Mech. 40, 185–208.Google Scholar
Ng, C. S., Ooi, A., Lohse, D. & Chung, D. 2015 Vertical natural convection: application of the unifying theory of thermal convection. J. Fluid Mech. 764, 349–361.CrossRefGoogle Scholar
Rossby, H. T. 1965 On thermal convection driven by non-uniform heating from below: an experimental study. Deep Sea Res. 12, 9–16.Google Scholar
Scotti, A. & White, B. 2011 Is horizontal convection really ‘non-turbulent’? Geophys. Res. Lett. 38, L21609.CrossRefGoogle Scholar
Sheard, G. J. & King, M. P. 2011 Horizontal convection: effect of aspect ratio on Rayleigh number scaling and stability. Appl. Math. Model. 35, 1647.Google Scholar
Shishkina, O. 2007 The Neumann stability of high-order symmetric schemes for convection–diffusion problems. Sib. Math. J. 48, 1141–1146.Google Scholar
Shishkina, O. 2016 Momentum and heat transport scalings in laminar vertical convection. Phys. Rev. E 93, 051102 (R).Google Scholar
Shishkina, O., Grossmann, S. & Lohse, D. 2016 Heat and momentum transport scalings in horizontal convection. Geophys. Res. Lett. 43, 1219–1225.Google Scholar
Shishkina, O. & Horn, S. 2016 Thermal convection in inclined cylindrical containers. J. Fluid Mech. 790, R3.Google Scholar
Shishkina, O., Stevens, R. J. A. M., Grossmann, S. & Lohse, D. 2010 Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution. New J. Phys. 12, 075022.Google Scholar
Shishkina, O. & Wagner, S. 2016 Prandtl-number dependence of heat transport in laminar horizontal convection. Phys. Rev. Lett. 116, 024302.CrossRefGoogle ScholarPubMed
Siggers, J. H., Kerswell, R. R. & Balmforth, N. J. 2004 Bounds on horizontal convection. J. Fluid Mech. 517, 55–70.Google Scholar
Song, H. & Tong, P. 2010 Scaling laws in turbulent Rayleigh–Bénard convection under different geometry. Eur. Phys. Lett. 90, 44001.CrossRefGoogle Scholar
Stevens, R. J. A. M., van der Poel, E. P., Grossmann, S. & Lohse, D. 2013 The unifying theory of scaling in thermal convection: the updated prefactors. J. Fluid Mech. 730, 295–308.Google Scholar
Wang, W. & Huang, R. X. 2005 An experimental study on thermal circulation driven by horizontal differential heating. J. Fluid Mech. 540, 49–73.CrossRefGoogle Scholar
Yu, H., Li, N. & Ecke, R. E. 2007 Scaling in laminar natural convection in laterally heated cavities: is turbulence essential in the classical scaling of heat transfer? Phys. Rev. E 76, 026303.Google Scholar