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29 March 2024
 
  » arxiv » 1908.5837

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Universal fluctuations in the bulk of Rayleigh-B'enard turbulence
Yi-Chao Xie ; Bu-Ying-Chao Cheng ; Yun-Bing Hu ; Ke-Qing Xia ;
Date 16 Aug 2019
AbstractWe present an investigation of the root-mean-square (rms) temperature $sigma_T$ and the rms velocity $sigma_w$ in the bulk of Rayleigh-B’enard 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 $ heta_*$, the value of $sigma_T$ at the cell centre is a constant, i.e. $sigma_{T,c}/ heta_* approx 0.85$, over a wide range of the Rayleigh number ($10^{8}leq Raleq 10^{15}$) and the Prandtl number ($0.7leq Pr leq 23.34$), and is independent of the surface topographies of the top and bottom plates of the convection cell. A constant close to unity suggests that $ heta_*$ is a proper measure of the temperature fluctuation in the core region. On the other hand, $sigma_{w,c}/w_*$, the vertical rms velocity at the cell centre scaled by the convective velocity $w_*$, shows a weak $Ra$-dependence ($sim Ra^{0.07pm0.02}$) over $10^8leq Raleq 10^{10}$ at $Prsim4.3$ and is independent of plate topography. Similar to a previous finding by He & Xia ({it Phys. Rev. Lett.,} vol. 122, 2019, 014503), we find that the rms temperature profile $sigma_T(z)/ heta_*$ 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 rms velocity profile $sigma_w(z)/w_*$ obey a logarithmic dependence on $z$. The study thus demonstrates that the typical scales for the temperature and the velocity are the convective temperature $ heta_*$ and the the convective velocity $w_*$, respectively. Finally, we note that $ heta_*$ may be utilised to study the flow regime transitions in the ultra-high-$Ra$-number turbulent convection.
Source arXiv, 1908.5837
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