Verifying global stability of fluid flows despite transient growth of energy
Bibliographic record
Abstract
Verifying nonlinear stability of a laminar fluid flow against all perturbations is a classic challenge in fluid dynamics. All past results rely on monotonic decrease of a perturbation energy or a similar quadratic generalized energy. This "energy method" cannot show global stability of a flow in which perturbation energy may grow transiently. For the many flows that allow transient energy growth but seem to be globally stable (e.g. pipe flow and other parallel shear flows at certain Reynolds numbers) there has been no way to mathematically verify global stability. After explaining why the energy method was the only way to verify global stability of fluid flows for over 100 years, I will describe a different approach that is broadly applicable but more technical. This approach, proposed in 2012 by Goulart and Chernyshenko, uses sum-of-squares polynomials to computationally construct non-quadratic Lyapunov functions that decrease monotonically for all flow perturbations. I will present a computational implementation of this approach for the example of 2D plane Couette flow, where we have verified global stability at Reynolds numbers above the energy stability threshold. This energy stability result for 2D Couette flow had not been improved upon since being found by Orr in 1907. The results I will present are the first verification of global stability – for any fluid flow – that surpasses the energy method. This is joint work with Federico Fuentes (Universidad Católica de Chile) and Sergei Chernyshenko (Imperial College London).
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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 | 0.001 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| 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".