Unconditional Linear Stability of Plane Couette-Poiseuille Flow in Presence of Cross Flow
Bibliographic record
Abstract
We have investigated the linear stability of plane Couette-Poiseuille flow in the presence of a cross-flow. The base flow is characterised by the cross flow Reynolds number, Ri and the dimensionless wall velocity, k. Corresponding to each k ∈ [0,1], we have observed two ranges of Ri for which the flow is unconditionally linearly stable. In the lower range, we have a stabilisation of long wavelengths leading to a cut-off Ri. In this range, cross-flow stabilisation and Couette stabilisation appear to act via very similar mechanisms in this range, leading to the potential for robust compensatory design of flow stabilisation using either mechanism. As Ri is increased, we see first destabilisation and then stabilisation at very large Ri. The instability is again a long wavelength mechanism. A linear energy analysis reveals that in this range the Reynolds stress becomes amplified, the critical layer is irrelevant and viscous dissipation is completely dominated by the energy production/negation, which approximately balances at criticality.
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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 | 0.002 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".