Has the ultimate state of turbulent thermal convection been observed?

Abstract

An important question in turbulent Rayleigh-Bénard convection is the scaling of the Nusselt number with the Rayleigh number in the so-called ultimate state, corresponding to asymptotically high Rayleigh numbers. A related but separate question is whether the measurements support the so-called Kraichnan law, according to which the Nusselt number varies as the square root of the Rayleigh number (modulo a logarithmic factor). Although there have been claims that the Kraichnan regime has been observed in laboratory experiments with low aspect ratios, the totality of existing experimental results presents a conflicting picture in the highRayleigh-number regime. We analyse the experimental data to show that the claims on the ultimate state leave open an important consideration relating to non-Oberbeck-Boussinesq effects. Thus, the nature of scaling in the ultimate state of Rayleigh-Bénard convection remains open.

Thermal transfer in Rayleigh–Bénard cell with smooth or rough boundaries

“…This procedure is justified only by the broken symmetry of cell geometry. Indeed, though this has recently triggered some discussion (Skrbek & Urban, 2015;Shishkina et al, 2016), its relevance as a means to recover from non-Boussinesq effect is not discussed in this paper, because our working conditions are all chosen in a range where the Boussinesq approximation holds. The bulk temperature is not equal to (T h + T c )/2 due to the impedance adaptation of the flow induced by the introduction of roughness on only one plate of the cell.…”

Roughness as a Route to the Ultimate Regime of Thermal Convection

“…Experimental [12][13][14][15] and numerical [16][17][18] studies have found β ≈ 1/3. Chavanne et al [19] and He et al [20] have reported observing transitions to β = 0.39 and β = 0.38 in their respective experiments and these findings continue to stimulate discussion [21,22]. Motivated by studies of shear flow, Borue and Orszag [23] used pseudo-spectral methods at three resolutions (64 3 , 128 3 , 256 3 and hence values of Ra) to study "homogeneous" convection, in which the BL's are effectively removed.…”

Temperature profiles measurements in turbulent Rayleigh-Bénard convection by optical fibre system at the Barrel of II-menau

“…The shift of the side position profile to higher temperatures is expected as a result of upward convection flow near the side wall. The differences between the time-averaged temperatures T Pt (z) and the mean temperature T m in the region of turbulent core can be ascribed to the NOB effects [3,5]. The situation corresponds to the schematic illustration in Fig.…”

“…Breaking these conditions leads to Non-Oberbeck-Boussinesq (NOB) effects. e-mail: drahotsky@isibrno.cz The principal motivation of our long-term work is to shed light on the discrepancies among published results on heat transfer efficiency by RBC for Ra values above 10 11 [2][3][4] and influence of NOB effects on RBC, especially on a possible transition of RBC to the ultimate regime [5,6]. It was observed experimentally that NOB effects do lead to asymmetry of the thermal boundary layers adjacent to the EPJ Web of Conferences 180, 02020 (2018) https://doi.org/10.1051/epjconf/201818002020 EFM 2017 top and bottom plates (see schematic illustration in Fig.…”

“…It was observed experimentally that NOB effects do lead to asymmetry of the thermal boundary layers adjacent to the EPJ Web of Conferences 180, 02020 (2018) https://doi.org/10.1051/epjconf/201818002020 EFM 2017 top and bottom plates (see schematic illustration in Fig. 1), which subsequently alters the heat transfer efficiency at high Ra [5,7].…”