Testing Lagrangian Theories of Internal Wave Spectra. Part II: Varying the Number of Waves
Bibliographic record
Abstract
Abstract It has been proposed by Allen and Joseph, Hines, and Chunchuzov that the kinematic advection produced by superpositions of sinusoidal Lagrangian gravity waves confined to lower vertical wavenumbers m provides an explanation for the quasi-universal m−3 Eulerian spectral tails commonly found at higher m in the oceans and the atmosphere. In support of these theories, Hines has proposed a prototype wave spectrum claimed to meet criteria for Lagrangian linearity and the production of m−3 Eulerian spectra. Although the shape of the Lagrangian spectrum is claimed not to play a major role in this process, Hines has argued that moderately large numbers of waves are required to ensure quasilinear behavior in the Lagrangian frame. The present results demonstrate that, for amplitudes consistent with measurements of saturated waves in the middle atmosphere and for wavenumbers consistent with Hines’ prototype, adiabatic excesses do not diminish with increasing numbers of waves; in contrast, consistency with adiabatic constraints is only achieved in the limit of a single wave, for which the advective nonlinearity u · ∇ vanishes. Moreover, fields with strong singularities yield Eulerian tail slopes as large as −1.6, whereas those with lesser violations of adiabatic constraints yield Eulerian spectral tail slopes that are much steeper (more strongly negative) than −3. The implications for theories based on superpositions of Lagrangian sinusoidal waves, for the Hines quasilinear criteria, and for the Hines Doppler-spread theory and parameterization are addressed. The results are also relevant for experimentalists interested in spectral analysis of internal wave fields.
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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 | 0.004 | 0.018 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| 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 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".