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Boundary layer fluctuations in turbulent Rayleigh–Bénard convection

Published online by Cambridge University Press:  13 February 2018

Yin Wang ,
Wei Xu ,
Xiaozhou He ,
Hiufai Yik ,
Xiaoping Wang ,
Jörg Schumacher Open the ORCID record for Jörg Schumacher [Opens in a new window]  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
Wei Xu
Affiliation:
Nano Science and Technology Program, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Xiaozhou He
Affiliation:
Institute for Turbulence-Noise-Vibration Interaction and Control, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, China
Hiufai Yik
Affiliation:
Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Xiaoping Wang
Affiliation:
Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Jörg Schumacher
Affiliation:
Institut für Thermo- und Fluiddynamik, Postfach 100565, Technische Universität Ilmenau, D-98684 Ilmenau, Germany
Penger Tong*
Affiliation:
Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
*
†Email address for correspondence: [email protected]
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Abstract

We report a combined experimental and numerical study of the effect of boundary layer (BL) fluctuations on the scaling properties of the mean temperature profile $\unicode[STIX]{x1D703}(z)$ and temperature variance profile $\unicode[STIX]{x1D702}(z)$ in turbulent Rayleigh–Bénard convection in a thin disk cell and an upright cylinder of aspect ratio unity. Two scaling regions are found with increasing distance $z$ away from the bottom conducting plate. In the BL region, the measured $\unicode[STIX]{x1D703}(z)$ and $\unicode[STIX]{x1D702}(z)$ are found to have the scaling forms $\unicode[STIX]{x1D703}(z/\unicode[STIX]{x1D6FF})$ and $\unicode[STIX]{x1D702}(z/\unicode[STIX]{x1D6FF})$, respectively, with varying thermal BL thickness $\unicode[STIX]{x1D6FF}$. The functional forms of the measured $\unicode[STIX]{x1D703}(z/\unicode[STIX]{x1D6FF})$ and $\unicode[STIX]{x1D702}(z/\unicode[STIX]{x1D6FF})$ in the two convection cells agree well with the recently derived BL equations by Shishkina et al. (Phys. Rev. Lett., vol. 114, 2015, 114302) and by Wang et al. (Phys. Rev. Fluids, vol. 1, 2016, 082301). In the mixing zone outside the BL region, the measured $\unicode[STIX]{x1D703}(z)$ remains approximately constant, whereas the measured $\unicode[STIX]{x1D702}(z)$ is found to scale with the cell height $H$ in the two convection cells and follows a power law, $\unicode[STIX]{x1D702}(z)\sim (z/H)^{\unicode[STIX]{x1D716}}$, with the obtained values of $\unicode[STIX]{x1D716}$ being close to $-1$. Based on the experimental and numerical findings, we derive a new equation for $\unicode[STIX]{x1D702}(z)$ in the mixing zone, which has a power-law solution in good agreement with the experimental and numerical results. Our work demonstrates that the effect of BL fluctuations can be adequately described by the velocity–temperature correlation functions and the new BL equations capture the essential physics.

JFM classification

Boundary Layers: Boundary layer structure Turbulent Flows: Turbulence modelling
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 840 , 10 April 2018 , pp. 408 - 431
Copyright
© 2018 Cambridge University Press 

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