Transient and steady convection in two dimensions
Bibliographic record
Abstract
We simulate thermal convection in a two-dimensional square box using the no-slip condition on all boundaries, and isothermal bottom and top walls, and adiabatic sidewalls. We choose 0.1 and 1 for the Prandtl number $Pr$ and vary the Rayleigh number $Ra$ between $10^6$ and $10^{12}$ . We particularly study the temporal evolution of integral transport quantities towards their steady states. Perhaps not surprisingly, the velocity field evolves more slowly than the thermal field, and its steady state – which is nominal in the sense that large-amplitude low-frequency oscillations persist around plausible averages – is reached exponentially. We study these oscillation characteristics. The transient time for the velocity field to achieve its nominal steady state increases almost linearly with the Reynolds number. For large $Ra$ , the Reynolds number itself scales almost as $Ra^{2/3}\, Pr^{-1}$ , and the Nusselt number as $Ra^{2/7}$ .
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 source (direct Gemma or distilled Codex), 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".