Universal fluctuations in the bulk of Rayleigh–Bénard turbulence

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.

Rayleigh–Bénard convection in viscoelastic liquid bridges

“…the onset of buoyancy convection in systems uniformly heated from below and cooled from above, corresponding to the so-called Rayleigh-Bénard paradigm. This type of convection is known to produce such a variegated set of different structures and bifurcations that it has been considered for a long time as a universal testbed for the study of the typical properties of dissipative systems and their related evolution (Crespo del Arco et al 1988;Crespo Del Arco & Bontoux 1989;Clever & Busse 1993, 1994Gelfgat 1999;Delgado-Buscalioni, Crespo del Arco & Bontoux 2001;Xi, Lam & Xia 2004;Sun et al 2005;Lappa 2009;Xie et al 2019).…”

Coriolis effect on centrifugal buoyancy-driven convection in a thin cylindrical shell

“…of wall-normal velocity fluctuations in Rayleigh–Bénard convection. Xie, Hu & Xia (2019) observed that weakly depends on (). Here, our data of scale well with , without correction (figure 13 c ).…”

“…Another possibility could be due to the Coriolis force that is absent in Rayleigh–Bénard convection of Xie et al. (2019). Our data of scale well with (figure 13 d ).…”

“…For clarity, in (c,d) we only show the data points with Ro −1 L < 4 (below dashed-dotted grey line in panel a). The dotted line in panel (c) indicates the scalingKū max ∝ w 2 * Ra 0.14 based on the correction by Xie et al (2019). Figure 11(e-h) shows that Ro −1 L monotonically increases, by increasing Ra or Ro −1 , up to Ro −1 L 4.0.…”

“…Here, our data ofKū max scale well with w 2 * , without Ra correction (figure 13c). One possibility could be due to our unbounded (periodic) domain compared with the bounded (cylindrical or cubic) domains in Xie et al (2019). Another possibility could be due to the Coriolis force that is absent in Rayleigh-Bénard convection of Xie et al (2019).…”