Dynamics of Two Parallel Inverted Flags in Axial Flow
Bibliographic record
Abstract
Abstract Two identical thin flexible plates, referred to as “inverted flags”, in a side-by-side arrangement are investigated theoretically. A linear model is developed to predict the onset of instability. This linear model elucidates the mechanism of instability and the sensitivity of the critical flow velocity to the gap between the two flags. The dynamics of a single flag has been studied massively, but the coupling of multiple flags is seldom reported. The Euler-Bernoulli beam theory and incompressible potential flow theory are adopted in the model. The Galerkin method and Fourier transform technique are used to solve flag displacements and fluid potentials, respectively. As the flow velocity is increased, the first mode becomes unstable via a pitchfork bifurcation. At higher flow velocities, higher modes lose stability via Hopf bifurcations. Out-of-phase and in-phase motions are predicted for the two flags. It is found that the critical velocity is independent of the flag gap-to-length ratio when it is approximately greater than 1. When the ratio is reduced, the critical velocity becomes smaller. When the ratio is extremely small, flutter occurs to the first mode before static divergence.
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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 | 0.001 |
| 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".