On the asymptotic matching procedure predicting the formation number
Bibliographic record
Abstract
A detailed review of the asymptotic matching procedures predicting the formation number of vortex rings is presented. The original studies of Mohseni and Gharib [“A model for universal timescale of vortex ring formation,” Phys. Fluids 10(10), 2436–2438 (1998).], Shusser and Gharib [“A new model for inviscid vortex rings,” in 30th AIAA Fluid Dynamical Conference (1999).], and Linden and Turner [“The formation of ‘optimal’ vortex rings, and the efficiency of propulsion devices,” J. Mech. Fluids, 427, 61–72 (2001).] are applied to the extended slug-flow model for orifice starting jets and the Kaplanski model of isolated vortex rings. A predicted formation number of 3.5 in the modified non-dimensional time frame is found when the closure assumption in terms of the translational ring speed is chosen, which is consistent with experimental evidence. In addition, particle image velocimetry was performed to assess the validity of the closure assumptions of Mohseni and Gharib and Shusser and Gharib. First, it was further demonstrated that the modified slug-flow model provides an appropriate scaling for the kinematics of orifice-generated vortex rings. Second, the measurements provide experimental support to the method of Shusser and Gharib rather than the method of Mohseni and Gharib. This is further demonstrated by data extracted from the literature. To summarize, in order to predict the formation number, it is recommended to use the extended slug-flow model and the Kaplanski model of isolated vortex rings along with the closure assumption of Shusser and Gharib.
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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 | 0.006 | 0.022 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.004 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 0.003 |
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".