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Universal fluctuations in the bulk of Rayleigh–Bénard turbulence

Published online by Cambridge University Press:  06 September 2019

Yi-Chao Xie Open the ORCID record for Yi-Chao Xie [Opens in a new window] ,
Bu-Ying-Chao Cheng ,
Yun-Bing Hu  and
Ke-Qing Xia Open the ORCID record for Ke-Qing Xia [Opens in a new window]
Yi-Chao Xie*
Affiliation:
Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, PR China Center for Complex Flows and Soft Matter Research & Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, 518055, PR China
Bu-Ying-Chao Cheng
Affiliation:
Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, PR China
Yun-Bing Hu
Affiliation:
Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, PR China Center for Complex Flows and Soft Matter Research & Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, 518055, PR China
Ke-Qing Xia*
Affiliation:
Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, PR China Center for Complex Flows and Soft Matter Research & Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, 518055, PR China
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

We present an investigation of the root-mean-square (r.m.s.) temperature $\unicode[STIX]{x1D70E}_{T}$ and the r.m.s. velocity $\unicode[STIX]{x1D70E}_{w}$ in the bulk of Rayleigh–Bénard turbulence, using new experimental data from the current study and experimental and numerical data from previous studies. We find that, once scaled by the convective temperature $\unicode[STIX]{x1D703}_{\ast }$, the value of $\unicode[STIX]{x1D70E}_{T}$ at the cell centre is a constant ($\unicode[STIX]{x1D70E}_{T,c}/\unicode[STIX]{x1D703}_{\ast }\approx 0.85$) over a wide range of the Rayleigh number ($10^{8}\leqslant Ra\leqslant 10^{15}$) and the Prandtl number ($0.7\leqslant Pr\leqslant 23.34$), and is independent of the surface topographies of the top and bottom plates of the convection cell. A constant close to unity suggests that $\unicode[STIX]{x1D703}_{\ast }$ is a proper measure of the temperature fluctuation in the core region. On the other hand, $\unicode[STIX]{x1D70E}_{w,c}/w_{\ast }$, the vertical r.m.s. velocity at the cell centre scaled by the convective velocity $w_{\ast }$, shows a weak $Ra$-dependence (${\sim}Ra^{0.07\pm 0.02}$) over $10^{8}\leqslant Ra\leqslant 10^{10}$ at $Pr\sim 4.3$ and is independent of plate topography. Similar to a previous finding by He & Xia (Phys. Rev. Lett., vol. 122, 2019, 014503), we find that the r.m.s. temperature profile $\unicode[STIX]{x1D70E}_{T}(z)/\unicode[STIX]{x1D703}_{\ast }$ in the region of the mixing zone with a mean horizontal shear exhibits a power-law dependence on the distance $z$ from the plate, but now the universal profile applies to both smooth and rough surface topographies and over a wider range of $Ra$. The vertical r.m.s. velocity profile $\unicode[STIX]{x1D70E}_{w}(z)/w_{\ast }$ obeys a logarithmic dependence on $z$. The study thus demonstrates that the typical scales for the temperature and the velocity are the convective temperature $\unicode[STIX]{x1D703}_{\ast }$ and the convective velocity $w_{\ast }$, respectively. Finally, we note that $\unicode[STIX]{x1D703}_{\ast }$ may be utilised to study the flow regime transitions in ultrahigh-$Ra$-number turbulent convection.

JFM classification

Turbulent Flows: Turbulent convection
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 878 , 10 November 2019 , R1
Copyright
© 2019 Cambridge University Press 

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