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: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
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.
Parent problems
- Special case of Does the ultimate $\mathrm{Nu} \sim \mathrm{Ra}^{1/2}$ regime exist in Rayleigh-Benard convection? · open · from revision 1 The parent was revised since revision 1: it now states another question.
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