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Collective effect of thermal plumes on temperature fluctuations in a closed Rayleigh–Bénard convection cell

Published online by Cambridge University Press:  14 January 2022

Yin Wang Open the ORCID record for Yin Wang [Opens in a new window] ,
Yongze Wei ,
Penger Tong Open the ORCID record for Penger Tong [Opens in a new window]  and
Xiaozhou He Open the ORCID record for Xiaozhou He [Opens in a new window]
Yin Wang
Affiliation:
Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543, USA
Yongze Wei
Affiliation:
School of Mechanical Engineering and Automation, Harbin Institute of Technology, Shenzhen 518055, PR China
Penger Tong
Affiliation:
Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Xiaozhou He*
Affiliation:
School of Mechanical Engineering and Automation, Harbin Institute of Technology, Shenzhen 518055, PR China
*
†Email address for correspondence: hexiaozhou@hit.edu.cn
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Abstract

We report a systematic study of the collective effect of thermal plumes on the probability density function (p.d.f.) $P(\delta T)$ of temperature fluctuations $\delta T(t)$ in turbulent Rayleigh–Bénard convection. By decomposing $\delta T(t)$ into four basic fluctuation modes associated with single and multiple warm and cold plumes and a turbulent background, we derive an analytic form of $P(\delta T)$ based on the convolutions of the five independent modes. To test the derived form of $P(\delta T)$ in the multiple-plume regions, where the thermal plumes are heavily populated, we conduct time series measurements of temperature fluctuations in two convection cells; one is a vertical thin disk and the other is an upright cylinder of aspect ratio unity. For a given normalized position in most regions of the convection cell, all of the measured p.d.f.s $P(\delta T)$ for different Rayleigh numbers fall onto a single master curve, once $\delta T$ is normalized by its root-mean-square (r.m.s.) value $\sigma _T$. It is found that the measured $P(\delta T/\sigma _T)$ at different locations along the symmetric horizontal and vertical axes of the convection cells can all be well described by the derived form of $P(\delta T/\sigma _T)$. The fitted values of the parameters associated with the number of plumes in multiple plume clusters and their relative strengths and degrees of intermittency are closely linked to the spatial distribution of thermal plumes and local dynamics of the large-scale circulation in a closed convection cell. Our work thus provides a unified theoretical approach for understanding scalar p.d.f.s in a turbulent field, which is very useful not only for the present study but also for the study of many turbulent mixing problems of practical interest.

JFM classification

Convection: Plumes/thermals
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 934 , 10 March 2022 , A13
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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