Stability of stratified natural convection in a tall vertical annular cavity
Bibliographic record
Abstract
The stability of buoyancy-driven convection between vertical concentric cylinders is examined under vertical thermal stratification conditions, with a uniform temperature gap between the cylinders. Analytical solutions are derived for the parallel base flow. Critical Rayleigh numbers are determined from these solutions at various Prandtl numbers, stratification levels, and inner to outer radius ratios. Nonaxisymmetric critical disturbances can be found for low radius ratios and small Prandtl numbers, but are otherwise symmetric and usually occur in the form of travelling waves opposite to gravity, except at large Prandtl numbers and for strong stratification where the direction of propagation is reversed. The effect of curvature is to favor the onset of instability at any stratification level, for moderate and large Prandtl numbers. For small Prandtl numbers, curvature has a stabilizing effect at low stratification levels and is most influential at moderate levels. Computation of the Landau coefficient reveals that the bifurcations are at times subcritical, depending on the parameter values.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".