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

Journal Article · 14 January 2022 · Journal of Fluid Mechanics

DOI: https://doi.org/10.1017/jfm.2021.1107 · OSTI ID:1856186

Wang, Yin  ^[1]; Wei, Yongze ^[2]; Tong, Penger  ^[3]; He, Xiaozhou  ^[2]

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1. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
2. Harbin Institute of Technology, Shenzhen (China)
3. Hong Kong University of Science and Technology (HKUST) (Hong Kong)

Here, we report a systematic study of the collective effect of thermal plumes on the probability density function (PDF) P(δT) of temperature fluctuations δT(t) in turbulent Rayleigh-Benard convection. By decomposing δT(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(δT) based on the convolutions of the five independent modes. To test the derived form of P(δT) 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 PDFs P(δT) for different Rayleigh numbers fall onto a single master curve, once δT is normalized by its rms value σ_T . It is found that the measured P(δT /_σT ) 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(δT /_σT ). 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 PDFs 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.

• Research Organization: Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)
• Sponsoring Organization: USDOE; Hong Kong Research Grants Council; National Natural Science Foundation of China; National Natural Science Foundation of Guangdong Province; Science, Technology and Innovation Commission of Shenzhen Municipality; National Aeronautics and Space Administration (NASA); Max-Planck-Princeton Center for Plasma Physics
• Grant/Contract Number: AC02-09CH11466
• OSTI ID: 1856186
• Journal Information: Journal of Fluid Mechanics, Journal Name: Journal of Fluid Mechanics Vol. 934; ISSN 0022-1120
• Publisher: Cambridge University PressCopyright Statement
• Country of Publication: United States
• Language: English