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Universal fluctuations in the bulk of Rayleigh–Bénard turbulence

2019; Cambridge University Press; Volume: 878; Linguagem: Inglês

10.1017/jfm.2019.667

1469-7645

Yi-Chao Xie, Bu-Ying-Chao Cheng, Yun-Bing Hu, Ke‐Qing Xia,

Wind and Air Flow Studies

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.