Bibliographic record
Abstract
The flow of a planar jet (sheet) impinging onto a solid flat plate with slip is examined theoretically. The jet is assumed to spread out in a thin layer bounded by a hydraulic jump, and draining at the edge of the plate. In contrast to an adhering jet, a slipping jet does not admit a similarity solution. Taking advantage of the different scaling in each region, series expansions are used in the developing and fully viscous layers, which are matched at the transition point. We show that a slipping film exhibits a singularity in the normal stress at the leading edge of the boundary layer, as opposed to the singularity in velocity and shear stress for an adhering film. The boundary-layer and film heights are both found to decrease with slip relative to a smooth substrate, roughly like $\sqrt{30x/Re}-2S$ , whereas the slip velocity intensifies like $S\sqrt{Re/30x}$ with slip. Here, $x$ is the distance along the plate, $S$ is the slip length and $Re$ is the Reynolds number (in units of the jet width). The transition is delayed by slip. Guided by the measurements of Duchesne et al. ( Europhys. Lett. , vol. 107, 2014, p. 54002) for a circular adhering jet, the hydraulic-jump height and location are determined for a planar jet, and are found to increase with the Froude number (flow rate) like $Fr^{1/4}$ and $Fr^{5/8}$ respectively, essentially independently of slip length.
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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".