Primary Flow Transitions in the Baroclinic Annulus
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Bibliographic record
Abstract
This chapter discusses the effects that the Prandtl number has on the dynamics near the primary flow transition, i.e., the transition from the steady axisymmetric solution to rotating waves. It uses a dynamical systems approach that uses linear stability analysis, center manifold reduction, and normal forms to determine the behavior of the model equations near the primary transition. The chapter then describes the model equations and the methods involved in computing the primary transition curve, i.e., the curve in the parameter space that indicates where baroclinic instability sets in. It presents an example of a regime diagram for an experiment that uses water as the working fluid. Next, the chapter presents the nonlinear analysis and results for a wide range of Prandtl number. It concludes with a discussion of how the analysis can be extended to study the flow far from the transition, particularly, in the wave and vacillation regimes.
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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 | 0.001 |
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 it