Bibliographic record
Abstract
The dynamics of the atmospheric mesoscale and oceanic submesoscale are characterized by strong stratification and weak rotation, and the resulting energy spectra, though surprisingly universal, are still poorly understood. The aim of this work is to study the nonlinear dynamics and interactions of vortical motion (with potential vorticity) and internal inertia-gravity waves in the idealized context of homogeneous stratified turbulence, and to examine the extent to which they can account for the observations. We consider separately turbulence generated by vortical motion and internal waves using a combination of theory and numerical simulations. When vortical motion dominates the flow, the statistical mechanical equilibrium of the Boussinesq equations points to the absence of an inverse cascade of vortical energy. Instead, energy leaks into waves and cascades downscale. Our simulations show that the kz spectrum of vortical energy is flat out to kz ~ N/U (where N is the Brunt-Vaisala frequency and U is the root mean square velocity), which is consistent with the asymptotic limiting equations but not with the observations. Steeper spectra are obtained when waves are forced, but they are nevertheless shallower than the observations. At sufficiently strong stratifications, the wave energy spectra are found to be sensitive to the resolution of wave breaking and the presence of vortical motion. Bumpy spectra are obtained when no breaking occurs, but interactions with vortical modes cause the bumps to disappear. Overall, these results indicate that the observed atmosphere and ocean energy spectra are not universal properties of stratified turbulence, and theories for the spectra must take other factors into account. In both the vortical and wave-dominated cases, U/N emerges as a key vertical length scale. Overturning is generated only when U/N is larger than the dissipation scale. Furthermore, in the vortical case, it is the scale at which different layers are coupled together. When rotation is introduced, the coupling scale evolves from U/N to the quasi-geostrophic scale (f/N)L (where f is the Coriolis parameter and L is the horizontal scale). This transition occurs at a relatively large Rossby number of O(1).
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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 | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| 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 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".