Dynamics of the Forced Karman Wake: Comparison of 2D and 3D Models
Bibliographic record
Abstract
The interaction between the cylinder motion and the wake is a complex feedback phenomenon in which the symmetry relationship between the wake and the cylinder motion plays a key role. Depending on the frequency of oscillation the symmetry relationship between the unforced von Karman wake and the imposed forced oscillations can induce a series of bifurcations. This detailed bifurcation behavior is the subject of study in the present work. 2D and 3D simulations are carried out for a Reynolds number Re=1000. As the inline cylinder forcing amplitude is increased, the wake undergoes a series of bifurcations and associated changes in the flow structure. Although the 2D analysis is clearly non-physical, it leads to a ‘simpler’ and more tractable model. Detailed comparison of the 2D and 3D POD modes provides insight into the forced wake dynamics. The 3D spatial mode shapes are significantly similar to those from 2D simulations. The relative modal energy distribution captures well the wake flow complexity. The first mode contains over 90% of the flow energy in the 2D simulations. This ratio drops significantly in the 3D case to around 45%. Clearly 3D effects are very important when it comes to energy distribution between the modes. However, the predominance of the first mode seems high enough to maintain the 2D-like dynamics. The wake flow is found to undergo two main transitions with increased forcing. The first is periodic shedding to chaotic shedding. The second is chaotic shedding to half-frequency shedding caused by a period-doubling bifurcation. The 2D simulations correctly predict these bifurcations — including the type and the number of bifurcations. The results suggest that the forced wake dynamics are primarily dominated by two-dimensional rather than 3D dynamics. However, 3D effects are important in determining the exact parameter values where bifurcations occur. A previously developed low order analytical model, based on 2D simulations, is also used to predict the wake bifurcation behavior. The relevance of the low order model has interesting implications for VIV control.
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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".