Dynamics of Reduced Order Models of the Forced Karman Cylinder Wake
Bibliographic record
Abstract
Employing symmetry-group equivariant \nbifurcation theory discrete reduced order models for \nthe dynamics of the forced Karman wake have been \ndeveloped. It turns out that the bifurcation \nbehaviour of the complex forced wake flow can be \napproximately described by these simple models. \nAlthough the symmetry approach is highly \nconvenient when deriving the reduced order \nmodels, the general form of the resulting model \nrequires the extra step of determination of the \nmodel coefficients for a given physical flow. In \naddition, an important assumption of the approach \nabove is that symmetry holds exactly over the \ncomplete flow domain (and to infinity). In reality \nthis is not the case – particularly for flow assumed \nto have translational symmetry. \nThe present paper addresses these two \nconcerns. In a first attempt to obtain a physical \ninterpretation of the reduced order model \ncoefficients, the POD modes are employed in a \nGalerkin reduction of the complex Ginzburg- \nLandau (CGL) equation. The latter equation is a \nwell known approximate model for spatio-temporal \nflow dynamics. To account for imperfect flow field \nsymmetry, POD modes are derived directly from \nexperimental PIV measurements. \nAn analysis of the CGL-based reduced order \nmodel yields the key bifurcations of the \nsymmetrically forced Karman wake. Most \nimportantly the model confirms the saddle-node \nbifurcation, supporting the findings based on the \nsymmetry-based approach.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".