Stability and Bifurcation Analysis of a Forced Cylinder Wake
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Bibliographic record
Abstract
We present a study on the dynamics of a cylinder wake subjected to forced excitation. Williams et al. (1992) discovered that the spatial symmetry of the excitation plays a crucial role in determining the resulting wake dynamics. Reflection-symmetric forcing was found to affect the Karman wake much more strongly compared to Z2(κ, π) asymmetric forcing. For low forcing amplitudes, the existence of a nonlinear mode interaction mechanism was postulated to explain the observed “beating” phenomenon observed in the wake. Previous work by the authors (Mureithi et al. 2002, 2003) presented general forms of the modal interaction amplitude equations governing the dynamics of the periodically forced wake. In the present work, numerical CFD computations of the forced cylinder wake are presented. It is shown that the experimentally observed wake bifurcations can be reproduced by numerical simulations with reasonable accuracy. The CFD computations show that the forced wake first looses reflection symmetry followed by a bifurcation associated with vortex merging as the forcing amplitude is increased. A bifurcation analysis of a simplified amplitude equation shows that these two transitions are due to a pitchfork bifurcation and a period-doubling bifurcation of mixed mode solutions.
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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)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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