Linear stability of the Moore-Saffman model for a trailing wingtip vortex
Bibliographic record
Abstract
This paper presents an investigation of the stability of a trailing vortex using mean flow profiles given by an approximate solution of the Navier-Stokes equations. The axial and tangential velocity profiles obtained from this solution, deduced by Moore and Saffman [“Axial flow in laminar trailing vortices,” Proc. R. Soc. London, Ser. A 333, 491–508 (1973)], agree well with experiments involving wings at slight angles of attack. In particular, the Moore-Saffman profiles better describe the jet-like and wake-like axial flows near the center of the vortex than does the much-studied Batchelor vortex. We determine solutions numerically for these profiles and find that they are well suited to describe the flow at short and intermediate distances behind the wingtip. Growth rates for unstable perturbations are presented for different values of n, the wingtip loading parameter. These growth rates are shown to be somewhat larger than those obtained for the Batchelor vortex, and instability persists for larger values of the swirl. The largest amplification rates were found to occur near n = 0.5, the value corresponding to elliptic loading. This is within the range 0.44 < n < 1.0, where the core axial flow is wake-like. For n < 0.44, the flow in the vortex core is jet-like and the growth rates of unstable perturbations become progressively smaller, with all modes damped for n ≈ 0.25.
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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".