Principal instabilities of large amplitude inertio-gravity waves
Bibliographic record
Abstract
We analyze the three-dimensional stability properties of monochromatic, large-amplitude, nonhydrostatic inertio-gravity waves propagating in a rotating stratified fluid with no mean shear. The ratio of Coriolis parameter f to the Brunt-Väisälä frequency N is fixed at a value f/N=0.01, chosen to be representative of the Earth’s atmosphere and upper oceans in extra-tropical latitudes. By using Floquet theory combined with suitable coordinate transformations, our analysis provides an exact representation of the spatial and temporal periodicity of the basic wave state. Growth rates are computed for several discrete phase-elevation angles 80°⩽θ⩽89.7°, spanning the frequency range in which rotational effects become important, and the basic wave state changes from fully overturned to suboverturned. For each basic wave, we identify the growth rate peaks in disturbance wavenumber space—these are the principal modes. At the lowest phase-elevation angle considered, θ=80°, the dominant principal mode is similar to its low-frequency nonrotating counterpart, with disturbance roll axes aligned in, or nearly in, the direction of the largest component of basic wave shear. As θ increases to values where the effects of rotation are more strongly manifested, the dominant rotating mode shifts to oblique orientation. At still higher values of θ, the fastest-growing modes have roll axes oriented orthogonal to the main shear component of the basic wave. At the highest values of θ considered in this study, the waves are no longer vertically overturned, but still feature minimum Richardson numbers below 14. We find that such low-frequency waves are subject to wave-scale instabilities: for the largest amplitude considered, the instability shows no preferred orientation, while at a somewhat lower amplitude, the dominant instability prefers an oblique orientation. Dominant oblique instabilities have not been reported in previous approximate stability analyses of inertio-gravity waves, although they have been found in nonlinear simulations. Our analysis resolves this discrepancy.
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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) | 0.000 | 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.
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".