Elusive transition to the ultimate regime of turbulent RBC: Dynamics of LSC in high-Ra cryogenic helium experiments

Non Oberbeck-Boussinesq (NOB) effects may increase the heat transfer efficiency of turbulent Rayleigh-B\'enard convection (RBC), when the top plate temperature approaches the saturation vapor curve (SVC) even far away from the critical point of the working fluid. Our recent experimental study [1] using cryogenic $^4$He under conditions as close as possible to the Goettingen study using SF$_6$ [2] argues that the claim of having observed the transition to Kraichnan’s ultimate $Nu(Ra)$ scaling is likely due to NOB effects, and the important issue of transition to the ultimate state of RBC remains open. I will present here a detailed analysis of large-scale circulation (LSC) dynamics in the experiment [1]. I will discuss dependences of the Reynolds numbers associated with LSC circulation and sloshing and of the LSC reversal frequency on the position in the p-T diagram of $^4$He, in particular on the boundary layer asymmetry due to NOB conditions near the SVC. [1] P. Urban, P. Hanzelka, T. Králík, M. Macek, V. Musilová and L. Skrbek, Phys. Rev. E 99, 011101(R) (2019). [2] X. He, D. Funfschilling, H. Nobach, E. Bodenschatz, and G. Ahlers, Phys. Rev. Lett. 108, 024502 (2012).