Triad near-resonant instability of vertically bounded internal waves in non-uniform stratification
Bibliographic record
Abstract
Vertically bounded, horizontally propagating internal waves may become unstable through triad resonant instability, in which two sibling waves in background noise draw energy from a parent internal tide. If the background stratification is uniform, then the condition for pure resonance between the parent and sibling wave frequencies and horizontal and vertical wavenumbers can be found semi-analytically from the roots of a polynomial expression. In non-uniform stratification, determining the frequencies and horizontal wavenumbers for which resonance occurs is less straightforward. We develop a theory for near-resonant excitation of a pair of sibling waves from a low-mode internal wave in which the proximity to pure resonance is characterised by the discrepancy between the forced sibling wave frequencies and the natural frequency of these modes. Knowing this discrepancy can be used methodically to determine pure resonance conditions. This inviscid theory is compared with numerical simulations of effectively inviscid waves. For comparison with laboratory experiments, the theory is adapted to include viscous effects both in the bulk of the fluid and at the side walls of the tank. We find that our theoretical predictions for frequencies and wavenumbers of the fastest growing sibling waves are generally consistent between theory, simulations and experiments, though theory overpredicts the growth rate observed in experiments. In all cases, the growth rate of sibling waves decreases with decreasing parent wave frequency, becoming negligibly small in experiments if the parent wave has frequency less than $\approx 0.7$ of the buoyancy frequency at the surface.
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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 | 0.000 | 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".