The onset of transient turbulence in minimal plane Couette flow
Bibliographic record
Abstract
The onset of transient turbulence in minimal plane Couette flow has been identified theoretically as homoclinic tangency with respect to a simple edge state for the Navier–Stokes equation, i.e., the gentle periodic orbit (the lower branch of a saddle-node pair) found by Kawahara & Kida ( J. Fluid Mech. , vol. 449, 2001, pp. 291–300). The first tangency of a pair of distinct homoclinic orbits to this periodic edge state has been discovered at Reynolds number $Re\equiv Uh/\unicode[STIX]{x1D708}=Re_{T}\approx 240.88$ ( $U$ , $h$ , and $\unicode[STIX]{x1D708}$ being half the difference of the two wall velocities, half the wall separation, and the kinematic viscosity of fluid, respectively). At $Re>Re_{T}$ a Smale horseshoe appears on the Poincaré section through transversal homoclinic points to generate a transient chaos that eventually relaminarises. In numerical experiments a sustaining chaos, which is a consequence of period-doubling cascade stemming from the upper branch of another saddle-node pair of periodic orbits, is observed in a narrow range of the Reynolds number, $Re\approx 240.40$ –240.46. At the upper edge of this $Re$ range it is found that the chaotic set touches the lower branch of this pair, i.e., another edge state. The corresponding chaotic attractor is replaced by a chaotic saddle at $Re\approx 240.46$ , and subsequently this saddle touches the gentle periodic edge state on the boundary of the laminar basin at the tangency Reynolds number $Re=Re_{T}$ . After this crisis on the boundary of the laminar basin, for $Re>Re_{T}$ , chaotic transients that eventually relaminarise can be observed.
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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 | 0.001 | 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".