Universal fluctuations in the bulk of Rayleigh-Benard turbulence

We present an investigation of the root-mean-square (r.m.s.) temperature sigma(T) and the r.m.s. velocity sigma(w) in the bulk of Rayleigh-Benard 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 theta(*), the value of sigma(T) at the cell centre is a constant (sigma(T,c)/theta(*) approximate to 0.85) over a wide range of the Rayleigh number (10(8) <= Ra <= 10(15)) and the Prandtl number (0.7 <= Pr <= 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 theta(*) is a proper measure of the temperature fluctuation in the core region. On the other hand, sigma(w,c)/w(*), the vertical r.m.s. velocity at the cell centre scaled by the convective velocity w(*), shows a weak Ra-dependence (similar to Ra-0.07 +/- 0.02) over 10(8) <= Ra <= 10(10) at Pr similar to 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 sigma(T)(z)/theta(*) 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 sigma(w)(z)/w(*) obeys a logarithmic dependence on z. The study thus demonstrates that the typical scales for the temperature and the velocity are the convective temperature theta(*) and the convective velocity w(*), respectively. Finally, we note that theta(*) may be utilised to study the flow regime transitions in ultrahigh-Ra-number turbulent convection.