Inertial instabilities of stratified jets: Linear stability theory
Bibliographic record
Abstract
This paper uses a linear stability analysis to investigate instabilities of barotropic and baroclinic jets that satisfy the necessary condition for inerital instabilities within the context of a rotating, stratified Boussinesq model. First, we review the different types of instabilities that can occur in these jets and the conditions that make the jet subject to inertial instability but stable to Rayleigh–Taylor instability. Second, we numerically solve one-dimensional and two-dimensional eigenvalue problems for the linear stability problems and examine the dependence of the growth rates on the Rossby number, Burger number, the aspect ratio, and the Reynolds number. We find that there are two critical Reynolds numbers where there is a transition between what type of instability has the largest growth rate. Finally, we examine the characteristics of inertial instabilities in more detail for three selected parameter sets: a low Reynolds number regime, a high Reynolds number regime, and a regime with low Reynolds number and larger aspect ratio. The most unstable mode in the low Reynolds number regime is a barotropic–baroclinic instability and has a barotropic spatial structure. In contrast, the most unstable mode in the high Reynolds number regime is an inertial instability and its spatial structure is independent of the along-flow direction. Modes with this property are commonly referred to as symmetric instabilities. In the intermediate regime, the flow can be unstable to both barotropic–baroclinic and inertial instabilities, possibly with comparable growth rates.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 | 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) | 0.002 | 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".