Skip to main content
SpringerLink
Log in

Similarities between 2D and 3D convection for large Prandtl number

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

Using direct numerical simulations of Rayleigh–Bénard convection (RBC), we perform a comparative study of the spectra and fluxes of energy and entropy, and the scaling of large-scale quantities for large and infinite Prandtl numbers in two (2D) and three (3D) dimensions. We observe close similarities between the 2D and 3D RBC, in particular, the kinetic energy spectrum E u (k)∼k −13/3, and the entropy spectrum exhibits a dual branch with a dominant k −2 spectrum. We showed that the dominant Fourier modes in 2D and 3D flows are very close. Consequently, the 3D RBC is quasi-two-dimensional, which is the reason for the similarities between the 2D and 3D RBC for large and infinite Prandtl numbers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13

Similar content being viewed by others

References

  1. G Ahlers, S Grossmann and D Lohse, Rev. Mod. Phys. 81, 503 (2009)

    Article  ADS  Google Scholar 

  2. J Schmalzl, M Breuer and U Hansen, Geophys. Astrophys. Fluid Dyn. 96, 381 (2002)

    Article  ADS  Google Scholar 

  3. J Schmalzl, M Breuer and U Hansen, Europhys. Lett. 67, 390 (2004)

    Article  ADS  Google Scholar 

  4. E P van der Poel, R J A M Stevens and D Lohse, J. Fluid Mech. 736, 177 (2013)

    Article  ADS  Google Scholar 

  5. D Lohseand and K Q Xia, Annu. Rev. Fluid Mech. 42, 335 (2010)

    Article  ADS  Google Scholar 

  6. S Grossmann and D Lohse, Phys. Rev. A 46, 903 (1992)

    Article  ADS  Google Scholar 

  7. V S L’vov, Phys. Rev. Lett. 67, 687 (1991)

    Article  ADS  Google Scholar 

  8. V S L’vov and G Falkovich, Physica D 57, 85 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  9. S Toh and E Suzuki, Phys. Rev. Lett. 73, 1501 (1994)

    Article  ADS  Google Scholar 

  10. A P Vincent and D A Yuen, Phys. Rev. E 60, 2957 (1999)

    Article  ADS  Google Scholar 

  11. A P Vincent and D A Yuen, Phys. Rev. E 61, 5241 (2000)

    Article  ADS  Google Scholar 

  12. P K Mishra and M K Verma, Phys. Rev. E 81, 056316 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  13. A Pandey, M K Verma and P K Mishra, Phys. Rev. E 89, 023006 (2014)

    Article  ADS  Google Scholar 

  14. G Silano, K R Sreenivasan and R Verzicco, J. Fluid Mech. 662, 409 (2010)

    Article  Google Scholar 

  15. M K Verma, A G Chatterjee, K S Reddy, R K Yadav, S Paul, M Chandra and R Samtaney, Pramana – J. Phys. 81, 617 (2013)

    Article  ADS  Google Scholar 

  16. P F Fischer, J. Comp. Phys. 133(1), 84 (1997)

    Article  ADS  Google Scholar 

  17. M Chandra and M K Verma, Phys. Rev. Lett. 110, 114503 (2013)

    Article  ADS  Google Scholar 

  18. N K Vitanov, Phys. Lett. A 248, 338 (1998)

    Article  ADS  Google Scholar 

  19. M K Verma, Phys. Rep. 401, 229 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  20. G Boffetta and R E Ecke, Annu. Rev. Fluid Mech. 44, 427 (2012)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The numerical simulations were performed at HPC and Newton clusters of IIT Kanpur, and at Param Yuva cluster of CDAC Pune. This work was supported by a research grant SERB /F/3279/2013-14 from Science and Engineering Research Board, India. The authors thank Supriyo Paul for useful comments and sharing his earlier results on 2D RBC. The authors also thank A Kumar for providing help in flow visualization.

Author information

Authors and Affiliations

  1. Department of Physics, Indian Institute of Technology, Kanpur, 208 016, India

    AMBRISH PANDEY, MAHENDRA K VERMA, ANANDO G CHATTERJEE & BIPLAB DUTTA

Authors
  1. AMBRISH PANDEY
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. MAHENDRA K VERMA
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. ANANDO G CHATTERJEE
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. BIPLAB DUTTA
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to AMBRISH PANDEY.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

PANDEY, A., VERMA, M.K., CHATTERJEE, A.G. et al. Similarities between 2D and 3D convection for large Prandtl number. Pramana - J Phys 87, 13 (2016). https://doi.org/10.1007/s12043-016-1204-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12043-016-1204-z

Keywords

PACS Nos

Search

Navigation