On the Existence of Solitary Wave Solutions to the Shallow-Water Equations on the f Plane
Bibliographic record
Abstract
Abstract In a recent paper Li argued that the inviscid shallow-water equations on the f plane exhibit a class of zonally propagating solitary wave solutions, referred to by the author as “geosolitary waves.” These solutions have propagation speeds that are slower than the shallow-water speed gH, and as constructed by Li, have a cusp in the height and zonal velocity field at the origin. The meridional velocity is found to be discontinuous at the origin, though its magnitude is much smaller than the magnitude of the zonal velocity. The authors reconsider the existence of geosolitary waves from the point of view of dynamical system theory and demonstrate that the cusp discontinuity at the origin is an unavoidable property of the solutions. Moreover, it is shown that, in contrast to suggestions made by Li, adding viscosity and diffusivity does not yield smooth, bounded solitary wave solutions. Last, the reason why geosolitary waves cannot be expected to exist in a continuously stratified fluid is discussed.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 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".