Gravity-driven flow over heated, porous, wavy surfaces
Why this work is in the frame
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Bibliographic record
Abstract
The method of weighted residuals for thin film flow down an inclined plane is extended to include the effects of bottom waviness, heating, and permeability in this study. A bottom slip condition is used to account for permeability and a constant temperature bottom boundary condition is applied. A weighted residual model (WRM) is derived and used to predict the combined effects of bottom waviness, heating, and permeability on the stability of the flow. In the absence of bottom topography, the results are compared to theoretical predictions from the corresponding Benney equation and also to existing Orr-Sommerfeld predictions. The excellent agreement found indicates that the model does faithfully predict the theoretical critical Reynolds number, which accounts for heating and permeability, and these effects are found to destabilize the flow. Floquet theory is used to investigate how bottom waviness influences the stability of the flow. Finally, numerical simulations of the model equations are also conducted and compared with numerical solutions of the full Navier-Stokes equations for the case with bottom permeability. These results are also found to agree well, which suggests that the WRM remains valid even when permeability is included.
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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