Global dynamics of Base- and Mean-flows: the case of the cylinder and an open cavity
Bibliographic record
Abstract
In the case of a cylinder flow, Barkley (EuroPhys. Lett 75, 2006) has shown, thanks to a global mode analysis, that the mean-flow was marginally stable and that the eigenfrequencies associated to the global modes well fit the Von-Karman Strouhal(Re) function for 46 < Re < 180. The aim of this article is to give a theoretical proof of this result. For this, we achieve a weakly non-linear analysis valid in the vicinity of the critical Reynolds number and based on the small parameter eps = Rec^(-1)-Re^(-1) << 1. We numerically compute the complex constants lambda; and mu' which appear in the Stuart-Landau Amplitude equation: dA/dt = eps*lambda* A-eps*mu'*A*|A|^2. Here A is the scalar complex amplitude of the marginally stable global mode existing at eps > 0 and which becomes unstable for eps > 0. If one looks carefully to the non-linear interactions yielding to mu';, we have shown that 1/ the mean-flow is stable 2/ the linear dynamics of the mean-flow yields the frequency of the saturated Stuart-Landau limit cycle. We will show that this result is not general by studying the case of an open cavity.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.004 | 0.001 |
| 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 | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".