Hydraulic control of homogeneous shear flows
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Bibliographic record
Abstract
If a shear flow of a homogeneous fluid preserves the shape of its velocity profile, a standard formula for the condition for hydraulic control suggests that this is achieved when the depth-averaged flow speed is less than ( gh ) 1/2 . On the other hand, shallow-water waves have a speed relative to the mean flow of more than ( gh ) 1/2 , suggesting that information could propagate upstream. This apparent paradox is resolved by showing that the internal stress required to maintain a constant velocity profile depends on flow derivatives along the channel, thus altering the wave speed without introducing damping. By contrast, an inviscid shear flow does not maintain the same profile shape, but it can be shown that long waves are stationary at a position of hydraulic control.
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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) | 0.000 | 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