### Abstract

New measurements of the Nusselt number have been made in turbulent thermal convection confined in a cylindrical container of aspect ratio unity. The apparatus is essentially the same as that used by Niemela et al. (2000), except that the height was halved. The measurement techniques were also identical but the mean temperature of the flow was held fixed for all Rayleigh numbers. The highest Rayleigh number was 2 × 10^{15}. Together with existing data, the new measurements are analysed with the purpose of understanding the relation between the Nusselt number and the Rayleigh number, when the latter is large. In particular, the roles played by Prandtl number, aspect ratio, mean wind, boundary layers, sidewalls, and non-Boussinesq effects are discussed. Nusselt numbers, measured at the highest Rayleigh numbers for which Boussinesq conditions hold and sidewall forcing is negligible, are shown to vary approximately as a 1/3-power of the Rayleigh number. Much of the complexity in interpreting experimental data appears to arise from aspects of the mean flow, including complex coupling of its dynamics to sidewall boundary conditions of the container. Despite the obvious practical difficulties, we conclude that the next generation of experiments will be considerably more useful if they focus on large aspect ratios.

Original language | English (US) |
---|---|

Pages (from-to) | 355-384 |

Number of pages | 30 |

Journal | Journal of Fluid Mechanics |

Issue number | 481 |

DOIs | |

State | Published - Apr 25 2003 |

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### ASJC Scopus subject areas

- Computational Mechanics
- Mechanics of Materials
- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*Journal of Fluid Mechanics*, (481), 355-384. https://doi.org/10.1017/S0022112003004087

**Confined turbulent convection.** / Niemela, J. J.; Sreenivasan, K. R.

Research output: Contribution to journal › Article

*Journal of Fluid Mechanics*, no. 481, pp. 355-384. https://doi.org/10.1017/S0022112003004087

}

TY - JOUR

T1 - Confined turbulent convection

AU - Niemela, J. J.

AU - Sreenivasan, K. R.

PY - 2003/4/25

Y1 - 2003/4/25

N2 - New measurements of the Nusselt number have been made in turbulent thermal convection confined in a cylindrical container of aspect ratio unity. The apparatus is essentially the same as that used by Niemela et al. (2000), except that the height was halved. The measurement techniques were also identical but the mean temperature of the flow was held fixed for all Rayleigh numbers. The highest Rayleigh number was 2 × 1015. Together with existing data, the new measurements are analysed with the purpose of understanding the relation between the Nusselt number and the Rayleigh number, when the latter is large. In particular, the roles played by Prandtl number, aspect ratio, mean wind, boundary layers, sidewalls, and non-Boussinesq effects are discussed. Nusselt numbers, measured at the highest Rayleigh numbers for which Boussinesq conditions hold and sidewall forcing is negligible, are shown to vary approximately as a 1/3-power of the Rayleigh number. Much of the complexity in interpreting experimental data appears to arise from aspects of the mean flow, including complex coupling of its dynamics to sidewall boundary conditions of the container. Despite the obvious practical difficulties, we conclude that the next generation of experiments will be considerably more useful if they focus on large aspect ratios.

AB - New measurements of the Nusselt number have been made in turbulent thermal convection confined in a cylindrical container of aspect ratio unity. The apparatus is essentially the same as that used by Niemela et al. (2000), except that the height was halved. The measurement techniques were also identical but the mean temperature of the flow was held fixed for all Rayleigh numbers. The highest Rayleigh number was 2 × 1015. Together with existing data, the new measurements are analysed with the purpose of understanding the relation between the Nusselt number and the Rayleigh number, when the latter is large. In particular, the roles played by Prandtl number, aspect ratio, mean wind, boundary layers, sidewalls, and non-Boussinesq effects are discussed. Nusselt numbers, measured at the highest Rayleigh numbers for which Boussinesq conditions hold and sidewall forcing is negligible, are shown to vary approximately as a 1/3-power of the Rayleigh number. Much of the complexity in interpreting experimental data appears to arise from aspects of the mean flow, including complex coupling of its dynamics to sidewall boundary conditions of the container. Despite the obvious practical difficulties, we conclude that the next generation of experiments will be considerably more useful if they focus on large aspect ratios.

UR - http://www.scopus.com/inward/record.url?scp=0038662675&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038662675&partnerID=8YFLogxK

U2 - 10.1017/S0022112003004087

DO - 10.1017/S0022112003004087

M3 - Article

AN - SCOPUS:0038662675

SP - 355

EP - 384

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

IS - 481

ER -