Stability of plane Couette–Poiseuille flow of shear-thinning fluid
Bibliographic record
Abstract
A linear stability analysis of the combined plane Couette and Poiseuille flow of shear-thinning fluid is investigated. The rheological behavior of the fluid is described using the Carreau model. The linearized stability equations and their boundary conditions result in an eigenvalue problem that is solved numerically using a Chebyshev collocation method. A parametric study is performed in order to assess the roles of viscosity stratification and the Couette component. First of all, it is shown that for shear-thinning fluid, the critical Reynolds number for a two-dimensional perturbation is less than for a three dimensional. Therefore, it is sufficient to deal only with a modified Orr–Sommerfeld equation for the normal velocity component. The influence of the velocity of the moving wall on the critical conditions is qualitatively similar to that for a Newtonian fluid. Concerning the effect of the shear thinning, the computational results indicate that this behavior leads to a decrease in the phase velocity of the traveling waves and an increase in stability, when an appropriate viscosity is used in the definition of the Reynolds number. Using a long-wave version of the Orr–Sommerfeld equation, the cutoff velocity is derived. The mechanisms responsible for the changes in the flow stability are discussed in terms of the location of the critical layers, Reynolds stress distribution, and the exchange of energy between the base flow and the disturbance.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 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 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".