Ultimate Turbulent Thermal Convection
While there is good agreement and understanding of the dependences Nu(Ra, Pr,Γ) in RBC for the “classical regime” (up to Ra ∼ 1011), for even larger Ra in the so-called ultimate regime of RBC the experimental results and their interpretations are more diverse. Understanding of this transition of the flow to the ultimate regime is of the utmost importance for extrapolating the heat transfer to large or strongly thermally driven systems. In O. Shishkina and D. Lohse, Phys. Rev. Lett. 133, 144001 (2024), a new scaling model for the ultimate regime in RBC was proposed, which distinguishes between four subregimes (see figure below). The model is consistent with the experimental data on Nu(Ra, Pr,Γ) of various large-Ra RBC experiments. In this new representation, which takes the Pr dependence into account, the onset of the ultimate regime is seen in all high-Ra experimental datasets, though at different Ra, as to be expected for a non-normal- nonlinear instability (R. E. Ecke, X. Zhang, and O. Shishkina, Phys. Rev. Fluids 7, L011501 (2022), X. Zhang, P. Reiter, O. Shishkina and R. E. Ecke, Phys. Rev. Fluids 9, 053501 (2024).
Our findings in G. Ahlers, E. Bodenschatz, R. Hartmann, X. He, D. Lohse, P. Reiter, R. J. A. M. Stevens, R. Verzicco, M.Wedi, S.Weiss, X. Zhang, L. Zwirner, and O. Shishkina, Phys. Rev. Lett. 128, 084501 (2022) predict also the Γ-dependence of the onset of the ultimate regime, which is consistent with almost Oberbeck–Boussinesq (OB) experiments and explains why, in small-Γ cells, much larger Ra must be achieved to observe the ultimate regime. The influence of the temperature- and pressuredependence of the fluid properties, i.e. the so-called non-OB effects, has been investigated in S. Weiss, M. S. Emran, and O. Shishkina, J. Fluid Mech. 986, R2 (2024). For cryogenic helium and pressurized SF6, the most popular fluids in high-Ra RBC measurements, the most critical residual is associated with the temperature dependence of specific heat at constant pressure (cp). Our DNS showed, however, that this feature alone cannot explain a sudden and intense enhancement in the heat transport in high-Ra experiments.