Asymptotic analysis of a surface-interfacial wave interaction
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Bibliographic record
Abstract
The three-dimensional interaction of a surface wave with two oblique interfacial waves in a horizontally infinite two-layer fluid is analyzed asymptotically. The nondimensional density difference is taken as a perturbation parameter and simple expressions for the growth rates and kinematic properties of the waves are obtained. The results show that the interfacial wavelengths are an order smaller than the surface wavelength. Also, to the leading-order approximation, the interfacial waves have a frequency half that of the surface wave, and their directions differ by 180° in the horizontal plane. The interaction coefficients are found to be equal at the leading order. The asymptotic solution is compared with the exact solution, and an excellent agreement is obtained for the range of applicability of the asymptotic theory. The analysis is extended to interactions in a medium with sidewalls. A previous laboratory flume study is addressed, and the asymptotic theory is used to explain the experimental observations.
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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 | 0.000 |
| 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) | 0.001 | 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 it