Chaotic response of the 2D semi-geostrophic and 3D quasi-geostrophic equations to gentle periodic forcing
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Bibliographic record
Abstract
Symmetries and Hamiltonian structure are combined with Melnikov's method to show a set of exact solutions to the 2D semi-geostrophic equations in an elliptical tank responding chaotically to gentle periodic forcing of the domain eccentricity (or of the potential vorticity, for that matter) which are sinusoidal in time with nearly any period. A similar approach confirms the chaotic response of the quasi-geostrophic equations to gentle periodic forcing by an external shearing field. Our approach simplifies and strengthens the proof by Bertozzi (upon which it is based) concerning the chaotic response of Kirchoff elliptical vortex patches to gentle shearing in the 2D Euler equations.
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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 | 0.001 |
| 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.
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