Elliptical instability of the Moore–Saffman model for a trailing wingtip vortex
Bibliographic record
Abstract
In this paper, we investigate the elliptical instability exhibited by two counter-rotating trailing vortices. This type of instability can be viewed as a resonance between two normal modes of a vortex and an external strain field. Recent numerical investigations have extended earlier results that ignored axial flow to include models with a simple wake-like axial flow such as the similarity solution found by Batchelor (J. Fluid Mech., vol. 20, 1964, pp. 645–658). We present herein growth rates of elliptical instability for a family of velocity profiles found by Moore & Saffman (Proc. R. Soc. Lond. A, vol. 333, 1973, pp. 491–508). These profiles have a parameter $n$ that depends on the wing loading. As a result, unlike the Batchelor vortex, they are capable of modelling both the jet-like and the wake-like axial flow present in a trailing vortex at short and intermediate distances behind a wingtip. Direct numerical simulations of the linearized Navier–Stokes equations are performed using an efficient spectral method in cylindrical coordinates developed by Matsushima & Marcus (J. Comput. Phys., vol. 53, 1997, pp. 321–345). We compare our results with those for the Batchelor vortex, whose velocity profiles are closely approximated as the wing loading parameter $n$ approaches 1. An important conclusion of our investigation is that the stability characteristics vary considerably with $n$ and $W_{0}$ , a parameter measuring the strength of the mean axial velocity component. In the case of an elliptically loaded wing ( $n=0.50$ ), we find that the instability growth rates are up to 50 % greater than those for the Batchelor vortex. Our results demonstrate the significant effect of the distribution and intensity of the axial flow on the elliptical instability of a trailing vortex.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".