Energy Spectra and Vorticity Dynamics in a Two-Layer Shallow Water Ocean Model
Bibliographic record
Abstract
Abstract The dynamically adaptive WAVETRISK-OCEAN global model is used to solve one- and two-layer shallow water ocean models of wind-driven western boundary current (WBC) turbulence. When the submesoscale is resolved, both the one-layer simulation and the barotropic mode of the two-layer simulations have an energy spectrum with a power law of −3, while the baroclinic mode has a power law of −5/3 to −2 for a Munk boundary layer. This is consistent with the theoretical prediction for the power laws of the barotropic and baroclinic (buoyancy variance) cascades in surface quasigeostrophic turbulence. The baroclinic mode has about 20% of the energy of the barotropic mode in this case. When a Munk–Stommel boundary layer dominates, both the baroclinic and barotropic modes have a power law of −3. Local energy spectrum analysis reveals that the midlatitude and equatorial jets have different energy spectra and contribute differently to the global energy spectrum. We have therefore shown that adding a single baroclinic mode qualitatively changes WBC turbulence, introducing an energy spectrum component typical of what occurs in stratified three-dimensional ocean flows. This suggests that the first baroclinic mode may be primarily responsible for the submesoscale turbulence energy spectrum of the oceans. Adding more vertical layers, and therefore more baroclinic modes, could strengthen the first baroclinic mode, producing a dual cascade spectrum (−5/3, −3) or (−3, −5/3) similar to that predicted by quasigeostrophic and surface quasigeostrophic models, respectively. Significance Statement This research investigates how wind energy is transferred from the largest ocean scales (thousands of kilometers) to the small turbulence scales (a few kilometers or less). We do this by using an idealized model that includes the simplest representation of density stratification. Our main finding is that this simple model captures an essential feature of the energy transfer process. Future work will compare our results to those obtained using ocean models with more realistic stratifications.
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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 | 0.001 |
| 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".