The fully nonlinear stratified geostrophic adjustment problem
Bibliographic record
Abstract
Abstract. The study of adjustment to equilibrium is a classical problem in geophysical fluid dynamics. We consider the fully nonlinear, stratified adjustment problem from a numerical point of view. We present results of smooth dam break simulations based on experiments in the published literature. We focus on both the wave trains that propagate away from the nascent geostrophic state and the geostrophic state itself. For the Rossby number range considered the rank ordered solitary wave train of the non rotating adjustment problem breaks down into a leading packet-like disturbance and a trailing tail. We consider variations in Rossby number and demonstrate that the wave train emanates from the inertial oscillations of the geostrophic state itself, but that the precise phase of the oscillation that yields the wave train is Rossby number dependent. We quantify the strength of the inertial oscillations of the geostrophic state and find results that are in agreement with hydrostatic theory in the literature. We consider the effects of changes in the polarity of the initial perturbations and find that the leading wave packet never completely separates from the trailing tail in this case. Finally we demonstrate that both polarities yield a unique signature in the spectrum of the depth averaged kinetic energy. This signature is fundamentally different from that found in non-rotating cases, and allows for low rotation rates allows for the discrimination between the polarity of the initial perturbation.
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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 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| 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".