Analytical and Chebyshev pseudospectral numerical solutions for a class of axisymmetric horizontal flows dominated by mass or heat sources
Bibliographic record
Abstract
SUMMARY A class of axisymmetric horizontal flows dominated by strong heat or mass sources are considered here, which systematically arise in multiscale atmospheric and oceanic flows in various spatiotemporal scales such as hurricane embryos. Various linear and nonlinear analytical solutions are proposed, and several examples are given to illustrate them. On the basis of the proposed exact solutions, stability of the flow under various conditions is examined. The proposed exact solutions serve as benchmarks for validation of numerical models. A Chebyshev pseudospectral model is also developed for these flows. The numerical results are compared with the developed analytical solutions as well as a high‐resolution numerical solution, which showed an excellent performance of the numerical model in terms of numerical diffusion and oscillation. The numerical method is also efficient because expensive calculations such as LU decomposition are only needed once, at the beginning of calculations. The model could be used in studying small‐scale and multiple‐scale phenomena such as hot towers and hurricane embryos, which are the subject of future studies. Copyright © 2011 John Wiley & Sons, Ltd.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".