The Dynamics of Quasigeostrophic Lens-Shaped Vortices
Bibliographic record
Abstract
Abstract The stability of lens-shaped vortices is revisited in the context of an idealized quasigeostrophic model. We compute the stability characteristics with higher accuracy and for a wider range of Burger numbers (Bu) than what was previously done. It is found that there are four distinct Bu regions of linear instability. Over the primary region of interest (0.1 < Bu < 10), we confirm that the first and second azimuthal modes are the only linearly unstable modes, and they are associated with vortex tilting and tearing, respectively. Moreover, the most unstable first azimuthal mode is not precisely captured by the linear stability analysis because of the extra condition that is imposed at the vortex center, and accurate calculations of the second azimuthal mode require higher resolution than was previously considered. We also study the nonlinear evolution of lens-shaped vortices in the context of this model and present the following results. First, vortices with a horizontal length scale a little less than the radius of deformation (Bu > 1) are barotropically unstable and develop a wobble, whereas those with a larger horizontal length scale (Bu < 1) are baroclinically unstable and often split. Second, the transfer of energy between different horizontal scales is quantified in two typical cases of barotropic and baroclinic instability. Third, after the instability the effective Bu is closer to unity.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 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 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".