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Turbulent temperature fluctuations in a closed Rayleigh–Bénard convection cell

Published online by Cambridge University Press:  04 July 2019

Yin Wang Open the ORCID record for Yin Wang [Opens in a new window] ,
Xiaozhou He  and
Penger Tong Open the ORCID record for Penger Tong [Opens in a new window]
Yin Wang
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, China
Penger Tong*
Affiliation:
Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
*
†Email address for correspondence: penger@ust.hk
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Abstract

We report a systematic study of spatial variations of the probability density function (PDF) $P(\unicode[STIX]{x1D6FF}T)$ for temperature fluctuations $\unicode[STIX]{x1D6FF}T$ in turbulent Rayleigh–Bénard convection along the central axis of two different convection cells. One of the convection cells is a vertical thin disk and the other is an upright cylinder of aspect ratio unity. By changing the distance $z$ away from the bottom conducting plate, we find the functional form of the measured $P(\unicode[STIX]{x1D6FF}T)$ in both cells evolves continuously with distinct changes in four different flow regions, namely, the thermal boundary layer, mixing zone, turbulent bulk region and cell centre. By assuming temperature fluctuations in different flow regions are all made from two independent sources, namely, a homogeneous (turbulent) background which obeys Gaussian statistics and non-uniform thermal plumes with an exponential distribution, we obtain the analytic expressions of $P(\unicode[STIX]{x1D6FF}T)$ in four different flow regions, which are found to be in good agreement with the experimental results. Our work thus provides a unique theoretical framework with a common set of parameters to quantitatively describe the effect of turbulent background, thermal plumes and their spatio-temporal intermittency on the temperature PDF $P(\unicode[STIX]{x1D6FF}T)$.

JFM classification

Turbulent Flows: Turbulent convection Mixing: Turbulent mixing

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JFM Papers
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Journal of Fluid Mechanics , Volume 874 , 10 September 2019 , pp. 263 - 284
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© 2019 Cambridge University Press 

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