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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 | Abstract: | We 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 | Services: | Forum | Review | PDF | Favorites |
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