A combined spectral-amplitude-perturbation approach for systematic mode selection in thermal convection
Bibliographic record
Abstract
Purpose – The post-critical convective state for Rayleigh-Benard (RB) convection is studied using a nonlinear spectral-amplitude-perturbation approach in a fluid layer heated from below. The paper aims to discuss these issues. Design/methodology/approach – In the spectral method the flow and temperature fields are expanded periodically along the layer and orthonormal shape functions are used in the transverse direction. A combined amplitude-perturbation approach is developed to solve the nonlinear spectral system in the post-critical range, even far from the linear stability threshold. Also, to leading order, the Lorenz model is recovered. Findings – It is found that very small Prandtl numbers (Pr < 0.1) can change the Nusselt number, when terms to O(ε5/2) and higher are considered. However, to lower orders the Prandtl number does not affect the results. Variation of the Nusselt number to different orders is found to be highly consistent. Comparison with experimental results is made and a very good qualitative agreement is observed, even far from the linear threshold. Originality/value – Unlike existing nonlinear formulations for RB thermal convection, the present combined spectral-perturbation approach provides a systematic method for mode selection. The number and type of modes to be included are directly related to the post-critical Rayleigh number. The method is not limited to the weakly nonlinear range.
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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".