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Universal fluctuations in the bulk of Rayleigh–Bénard turbulence
| Content Provider | Scilit |
|---|---|
| Author | Xie, Yi-Chao Cheng, Bu-Ying-Chao Hu, Yun-Bing Xia, Ke-Qing |
| Copyright Year | 2019 |
| 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. |
| Related Links | http://arxiv.org/pdf/1908.05837 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/64F9D61308CFDB84DCBA4F35ACACF5C7/S0022112019006670a.pdf/div-class-title-universal-fluctuations-in-the-bulk-of-rayleigh-benard-turbulence-div.pdf |
| ISSN | 00221120 |
| e-ISSN | 14697645 |
| DOI | 10.1017/jfm.2019.667 |
| Journal | Journal of Fluid Mechanics |
| Volume Number | 878 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2019-11-10 |
| Access Restriction | Open |
| Subject Keyword | Journal of Fluid Mechanics Fluids and Plasmas Physics Bénard Convection Turbulent Convection |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Mechanics of Materials Condensed Matter Physics Mechanical Engineering |
