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Turbulent thermal convection in a closed domain: viscous boundary layer and mean flow effects

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Abstract.

In this paper the effects of viscous boundary layers and mean flow structures on the heat transfer of a flow in a slender cylindrical cell are analysed using the direct numerical simulation of the Navier-Stokes equations with the Boussinesq approximation. Ideal flows are produced by suppressing the viscous boundary layers and by artificially enforcing the flow axisymmetry with the aim of checking some proposed explanations for the Nusselt number dependence on the Rayleigh number. The emerging picture suggests that, in this slender geometry,the presence of the viscous boundary layers does not have appreciable impact on the slope of the Nu vs. Ra relation while a transition of the mean flow is most likely the reason for the slope increase observed around Ra=2 x 109.

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References

  1. G. Ahlers , Phys. Rev. E 63, 015303 (2001)

    Article  Google Scholar 

  2. P.E. Roche, B. Castaing, B. Chabaud, B. Hebral, J. Sommeria, Eur. Phys. J. B 24, 405 (2001)

    Article  Google Scholar 

  3. J.J. Niemela, K.R. Sreenivasan, J. Fluid Mech. 481, 355 (2003)

    Article  Google Scholar 

  4. R. Verzicco, J. Fluid Mech. 473, 201 (2002)

    Article  MATH  Google Scholar 

  5. S. Chaumat, B. Castaing, F. Chillá, Rayleigh-Bénard cells: influence of the plate properties Advances in Turbulence IX, edited by I.P. Castro, P.E. Hancock, id:46,1 (CIMNE, Barcellona 2002)

  6. B. Castaing, G. Gunaratne, F. Heslot, L. Kadanoff., A. Libchaber, S. Thomae, X.Z. Wu, S. Zaleski, G. Zanetti, J. Fluid Mech. 204, 1 (1989)

    Google Scholar 

  7. B.I. Shraiman, E.D. Siggia, Phys. Rev. A 42, 3650 (1990)

    Article  Google Scholar 

  8. X. Chavanne, F. Chillá, B. Castaing, B. Hébral, B. Chabaud, J. Chaussy, Phys. Rev. Lett. 79, 3648 (1997)

    Article  Google Scholar 

  9. X. Chavanne, F. Chillá, B. Chabaud, B. Castaing, B. Hebral, Phys. Fluids 13, 1300 (2001)

    Google Scholar 

  10. P.E. Roche, B. Castaing, B. Chabaud, B. Hebral, Europhys. Lett. E 58, 693 (2002)

    Google Scholar 

  11. R. H. Kraichnan, Phys. Fluids 5, 1374 (1962)

    Google Scholar 

  12. S. Grossmann, D. Lohse, J. Fluid Mech. 407, 27 (2000)

    MATH  Google Scholar 

  13. S. Grossmann, D. Lohse Phys. Rev. Lett. 86, 3316 (2001)

    Google Scholar 

  14. R. Verzicco, R. Camussi, J. Fluid Mech. 477, 19 (2003)

    Google Scholar 

  15. X.Z. Wu, Along a Road to Developed Turbulence: Free Thermal Convection in Low Temperature Helium Gas, Ph.D. thesis, University of Chicago (1991)

  16. J.J. Niemela, L. Skrbek., R.R. Sreenivasan, R.J. Donnely, Nature 404, 837 (2000)

    Article  CAS  PubMed  Google Scholar 

  17. P.E. Roche, B. Castaing, B. Chabaud, B. Hebral, Phys. Rev. E 63, 045303-1-045303-4 (2001b)

    Google Scholar 

  18. G. Grötzbach, J. Comput. Phys. 49, 241 (1983)

    Google Scholar 

  19. G. Ahlers, X. Xu, Phys. Rev. Lett. 86, 3320 (2001)

    Google Scholar 

  20. K.Q. Xia, S. Lam, S.Q. Zhou, Phys. Rev. Lett. 88(6), 064501-1-4 (2002)

    Google Scholar 

  21. S. Grossmann, D. Lohse, Phys. Rev. E 66, 016305-1 - 016305-6 (2002)

    Google Scholar 

  22. T.H. Solomon, J.P. Gollub, Phys. Rev. Lett. 64, 2382 (1990)

    Google Scholar 

  23. T.H. Solomon, J.P. Gollub, Phys. Rev. A 43, 6683 (1991)

    Google Scholar 

  24. S. Ciliberto, S. Cioni, C. Laroche, Phys. Rev. E 54, 5901 (1996)

    Google Scholar 

  25. A. Umeura, F. Busse J. Fluid Mech. 208, 459 (1989)

    Google Scholar 

Download references

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Authors and Affiliations

  1. DIMeG and CEMeC, Politecnico di Bari, Via Re David 200, 70125, Bari, Italia

    R. Verzicco

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  1. R. Verzicco
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Correspondence to R. Verzicco.

Additional information

Received: 7 March 2003, Published online: 22 September 2003

PACS:

47.27.Te Convection turbulent flows - 47.32.-y Fluid flow buoyant - 44.25.+f Heat transfer convective

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Verzicco, R. Turbulent thermal convection in a closed domain: viscous boundary layer and mean flow effects. Eur. Phys. J. B 35, 133–141 (2003). https://doi.org/10.1140/epjb/e2003-00264-6

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  • DOI: https://doi.org/10.1140/epjb/e2003-00264-6

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