The planar spread of a liquid jet and hydraulic jump on a porous layer
Bibliographic record
Abstract
The flow of a planar liquid free surface jet impinging on a porous layer is theoretically examined, with particular emphasis on the influence of porosity ϕ, stress jump coefficient χ, and depth of the porous layer on the super- and sub-critical regions. Despite the numerous studies in the literature on the flow over a porous medium, the jet impingement on a porous layer has not been studied. An averaging integral approach is adopted to capture the flow in the developing boundary-layer and fully viscous regions upstream of the hydraulic jump. Asymptotic analyses for small distance from impingement, small porosity, and small porous layer depth are also conducted, elucidating the various mechanisms behind the behavior predicted numerically. We find a domain of validity for the stress jump coefficient χ in which numerical and experimental values of χ from the literature seem to fall. The transition point, where the outer edge of the boundary layer intersects the film surface, moves downstream with increasing porosity and stress jump coefficient accompanied by a drop in the film thickness. While the height of the hydraulic jump generally decreases with increasing ϕ for any permeability, the jump location decreases for small χ and increases for large χ.
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How this classification was reachedexpand
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".