A Baroclinic Instability that Couples Balanced Motions and Gravity Waves
Bibliographic record
Abstract
Abstract Normal modes of a linear vertical shear (Eady shear) are studied within the linearized primitive equations for a rotating stratified fluid above a rigid lower boundary. The authors' interest is in modes having an inertial critical layer present at some height within the flow. Below this layer, the solutions can be closely approximated by balanced edge waves obtained through an asymptotic expansion in Rossby number. Above, the solutions behave as gravity waves. Hence these modes are an example of a spatial coupling of balanced motions to gravity waves. The amplitude of the gravity waves relative to the balanced part of the solutions is obtained analytically and numerically as a function of parameters. It is shown that the waves are exponentially small in Rossby number. Moreover, their amplitude depends in a nontrivial way on the meridional wavenumber. For modes having a radiating upper boundary condition, the meridional wavenumber for which the gravity wave amplitude is maximal occurs when the tilts of the balanced edge wave and gravity waves agree.
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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 | 0.000 |
| Open science | 0.000 | 0.001 |
| 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 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".