Scaling of large-scale quantities in Rayleigh-Benard convection

Ambrish Pandey, Mahendra K. Verma

Research output: Contribution to journalArticlepeer-review

40 Scopus citations

Abstract

We derive a formula for the Péclet number (Pe) by estimating the relative strengths of various terms of the momentum equation. Using direct numerical simulations in three dimensions, we show that in the turbulent regime, the fluid acceleration is dominated by the pressure gradient, with relatively small contributions arising from the buoyancy and the viscous term; in the viscous regime, acceleration is very small due to a balance between the buoyancy and the viscous term. Our formula for Pe describes the past experiments and numerical data quite well. We also show that the ratio of the nonlinear term and the viscous term is ReRa-0.14, where Re and Ra are Reynolds and Rayleigh numbers, respectively, and that the viscous dissipation rate εu = (U3/d)Ra-0.21, where U is the root mean square velocity and d is the distance between the two horizontal plates. The aforementioned decrease in nonlinearity compared to free turbulence arises due to the wall effects.
Original languageEnglish (US)
Pages (from-to)095105
JournalPhysics of Fluids
Volume28
Issue number9
DOIs
StatePublished - Sep 16 2016
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2022-06-02
Acknowledgements: We thank Abhishek Kumar and Anando G. Chatterjee for discussions and help in simulations. We are grateful to the anonymous referees for important suggestions and comments on our manuscript. The simulations were performed on the HPC system and Chaos cluster of IIT Kanpur, India, and SHAHEEN-II supercomputer of KAUST, Saudi Arabia. This work was supported by Research Grant No. SERB/F/3279/2013-14 from the Science and Engineering Research Board, India.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

ASJC Scopus subject areas

  • Condensed Matter Physics

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