Circular hydraulic jump on finite surfaces with capillary limit
Bibliographic record
Abstract
A round liquid jet impinging on a circular disc with free edge generates a thin liquid film in the center surrounded by a thick film. For low flow rates, the thick film is bounded by a stable rim around the disc edge and flows off only from one spot at the edge. The outer Froude number remains constant for varied flow rates and disc sizes but changes with the surface tension of the fluid. The jump radius increases linearly with the flow rate, and the linear slope varies with the surface tension. Due to the stable-rim edge condition, the constant outer Froude numbers observed in our study are different from the constant value reported by Duchesne et al. [“Constant Froude number in a circular hydraulic jump and its implication on the jump radius selection,” Europhys. Lett. 107, 54002 (2014)]. Despite the constant outer Froude numbers being independent of the flow rate, the inner Froude number changes with the flow rate, which is due to the surface tension force at the jump location. Force analysis is conducted by taking into account the stable rim, and the derived equations provide the relationship of jump radius with the contact angle of the stable rim, disc size, and jet flow. The maximum outer Froude number and the minimum inner Froude number are theoretically analyzed. Depending on the pre-jump velocity profile and the surface tension force at the jump, the maximum outer Froude number could be larger than unity. The shape of free surface at the jump is analyzed to evaluate the theoretical assumption of steep jump.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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 source (direct Gemma or distilled Codex), 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".