FLUID In the literature: contested

What sets the Rayleigh number of the transition to ultimate convection?

In plain words

If the steep heat-transport regime exists, it starts at very different heating strengths in different experiments. What fixes the starting point is unknown.

Precise statement

Assuming a transition exists, determine how the onset Rayleigh number $Ra*$ depends on Pr, aspect ratio $\Gamma$, plate and sidewall conditions and residual perturbations, and whether onset corresponds to a universal critical shear Reynolds number $Re_{s}$ of the plate boundary layers (Grossmann-Lohse estimate $Re_{s} \sim 420$, approximately). Answer: a predictive criterion for $Ra*$, or a demonstration that the onset is a subcritical, perturbation-dependent transition with no single $Ra*$.

What would settle it

Systematic experiments in one apparatus varying $\Gamma$, Pr and controlled boundary-layer perturbations, mapping Ra* against $\mathrm{Re}_{s}$.

Status in the literature

Unverified note

Reported onsets range from $\mathrm{Ra}\sim 10^{11}$ to above $10^{14}$; Shishkina and Lohse (2024, arXiv:2407.16573) argue onset occurs in all large-Ra data sets at experiment-dependent Ra, as expected for a non-normal nonlinear instability.