No abstract

We present an investigation of the root-mean-square (rms) temperature σ T and the rms velocity σ 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 θ * , the value of σ T at the cell centre is a constant, i.e. σ T,c /θ * ≈ 0.85, over a wide range of the Rayleigh number (10 8 Ra 10 15 ) and the Prandtl number (0.7 P r 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 θ * is a proper measure of the temperature fluctuation in the core region. On the other hand, σ w,c /w * , the vertical rms velocity at the cell centre scaled by the convective velocity w * , shows a weak Ra-dependence (∼ Ra 0.07±0.02 ) over 10 8Ra 10 10 at P r ∼ 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 rms temperature profile σ T (z)/θ * 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 σ 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 θ * and the the convective velocity w * , respectively. Finally, we note that θ * may be utilised to study the flow regime transitions in the ultra-high-Ra-number turbulent convection.

The effect of centrifugal force in turbulent rotating Rayleigh–Bénard convection (RRBC) is studied experimentally in an aspect-ratio $\varGamma =1$ cylindrical convection cell and in the ranges of the Froude number $0.004\leq Fr \leq 0.363$ and the Rayleigh number $2.8\times 10^8 \leq Ra \leq 9.5\times 10^9$ , and with the Prandtl number fixed at $Pr=4.34$ . We use the bulk temperature anomaly to determine the onset Froude number $Fr_c$ , beyond which the centrifugal effects cannot be regarded as insignificant. It is found that $Fr_c$ depends on $Ra$ as $Fr_c\sim Ra^{0.53}$ , which may be understood qualitatively by the idea of local force balance. For $Fr>Fr_c$ , the centrifugal effect is more pronounced for smaller $Ra$ , which is also found for larger constant $1/Ro$ . This implies that the response of the system to the centrifugal force depends on the flow states, which, in RRBC, is mainly determined by the competition between the buoyancy and Coriolis forces. Detailed analysis of the sidewall temperature signal shows results consistent with those obtained from the bulk temperature. Based on the above results, we propose a different division of the $1/Ro$ – $Fr$ phase space than previously suggested. For the heat transport, the results under fixed $1/Ro$ show well-defined $Nu$ – $Ra$ scalings, which can provide a better prediction for the heat transport when extrapolating to the unexplored regions in the phase space.