Analytical solution for maximal frictional two-layer exchange flow
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Bibliographic record
Abstract
The maximal steady frictional exchange flow through a rectangular channel of constant width is analysed within the context of internal hydraulics. A one-dimensional analytical solution to the fully nonlinear problem of two-layer frictional exchange is developed and shown to compare well with experimental and field data. The analytical solution gives the maximal exchange flow rate and the variation in the height of the density interface along the channel for the case of zero barotropic forcing. In contrast to the assumed constant interface slope of previous theoretical formulations of frictional exchange flows, the resulting density interface is found to be nonlinear and asymmetric. Both interfacial and bottom friction play important roles in determining the exchange flow rate. It is shown that the frictional effects are important even in relatively short channels.
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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 | 0.001 | 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) | 0.000 | 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 it