Cryogenic Rayleigh–Bénard convection (RBC) at very high Rayleigh numbers (Ra) is a model system for studying buoyancy-driven flows and turbulent convective heat transport [1]. Of particular interest is the possible existence of the ultimate regime, characterized by an asymptotic heat-transfer scaling Nu ∝ Ra^1/2, and transition of the boundary layers to turbulence, which may occur via a non-normal nonlinear, and thus subcritical, transition [2].

We analyse new heat-transfer data obtained in Brno from two cylindrical cryogenic convection cells with aspect ratios Γ = 1 and 2 (diameter 0.3 m), covering the range Ra = 1E8–1E13. A transition in the heat-transfer scaling is observed at Ra ≈ 1E11. These results are compared with published high-Ra measurements from Göttingen using SF6 at ambient temperature in larger cells (diameter 1.12 m, Γ = 1, 0.5, and 0.33), where a corresponding transition has been reported at significantly higher Rayleigh numbers, Ra ≈ 1E13. In both experiments, the working points are located at similar positions in the p–T phase diagram relative to the critical point and the vapour–liquid saturation curve.

Remarkably, the heat-transfer efficiency in both data sets depends nearly uniquely on the dimensional parameter Ra/L^3, where L is the cell height, and remains largely independent of the aspect ratio [3]. The large discrepancy in the transition Rayleigh numbers between the Brno and Göttingen experiments therefore raises the question of whether the observed transition reflects (i) intrinsic ultimate-regime dynamics or (ii) is predominantly a manifestation of NOB effects and experimental imperfections or (iii) a non-normal nonlinear transition triggered by NOB fluid properties, which have not been excluded in recent comprehensive reviews [2].

Motivated by these considerations, we present a systematic analysis of experimental uncertainties and data-correction procedures relevant to Brno cryogenic RBC experiments, including parasitic heat leaks, adiabatic temperature-gradient effects, finite thermal conductivity of plates and sidewalls, NOB effects, and the selection of working points in the ⁴He p–T phase diagram based on available thermophysical property databases. Our results highlight the importance of rigorous uncertainty quantification when assessing evidence for the ultimate RBC regime [4].

This research was supported by grant No. 25-16812S of the Czech Science Foundation and by New York and Charles Universities.

[1] L. Skrbek, et al., Physics of Fluids 36 (2024).

[2] D. Lohse and O. Shishkina, Rev. Mod. Phys. 96, 035001 (2024).

[3] P. Urban, et al., Phys. Rev. Letters (2025) – under review.

[4] P. Urban, et al., JLTP (2026) – in preparation