Stability of Flow in a Channel with Drag Reducing Grooves
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Bibliographic record
Abstract
Laminar flow in a channel with longitudinal grooves is analyzed. Grooves may have an arbitrary shape but do not affect the average channel opening. It is demonstrated that there exist groove shapes that reduce the laminar drag. It is shown that the reduced geometry model based on a single Fourier mode captures the relevant flow characteristics with an acceptable accuracy. The linear stability analysis is used to determine the range of flow conditions when the flow remains laminar. The same grooves represent a certain class of surface roughness, and its effect of the critical flow conditions is of interest. It is demonstrated that the short wavelength grooves destabilize the flow while the long wavelength grooves have an opposite effect. Stability characteristics of the optimal grooves that produce the largest possible drag reduction have also been determined.
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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