A low-dimensional approach to nonlinear plane-Couette flow of viscoelastic fluids
Bibliographic record
Abstract
The nonlinear stability of the one-dimensional plane Couette flow is examined for a Johnson–Segalman fluid. The velocity and stress are represented by symmetric and antisymmetric Chandrasekhar functions in space. The flow field is obtained from the conservation and constitutive equations using the Galerkin projection method. Both inertia and normal stress effects are included. For given Reynolds number and viscosity ratio, two critical Weissenberg numbers are found at which an exchange of stability occurs between the Couette and other steady flows. The critical points coincide with the two extrema of the stress/rate-of-strain curve. At low (high) Reynolds number, the flow decays monotonically (oscillatorily) toward the steady-state solution. The number and stability of the nontrivial branches around the critical points are examined using the method of multiple scales. Comparison between the approximate and the numerical branches leads to excellent agreement in the vicinity of the critical points. The influence of the higher-order modes is assessed, showing low-order convergence and good accuracy when the flow profiles are compared against existing finite-element results.
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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".