On three-dimensional linear stability of Poiseuille flow of Bingham fluids
Bibliographic record
Abstract
Plane channel Poiseuille flow of a Bingham fluid is characterized by the Bingham number, B, which describes the ratio of yield and viscous stresses. Unlike purely viscous non-Newtonian fluids, which modify hydrodynamic stability studies only through the dissipation and the basic flow, inclusion of a yield stress additionally results in a modified domain and boundary conditions for the stability problem. We investigate the effects of increasing B on the stability of the flow, using eigenvalue bounds that incorporate these features. As B→∞ we show that three-dimensional linear stability can be achieved for a Reynolds number bound of form Re=O(B3/4), for all wavelengths. For long wavelengths this can be improved to Re=O(B), which compares well with computed linear stability results for two-dimensional disturbances [J. Fluid Mech. 263, 133 (1994)]. It is also possible to find bounds of form Re=O(B1/2), which derive from purely viscous dissipation acting over the reduced domain and are comparable with the nonlinear stability bounds in J. Non-Newt. Fluid Mech. 100, 127 (2001). We also show that a Squire-like result can be derived for the plane channel flow. Namely, if the equivalent eigenvalue bounds for a Newtonian fluid yield a stability criterion, then the same stability criterion is valid for the Bingham fluid flow, but with reduced wavenumbers and Reynolds numbers. An application of these results is to bound the regions of parameter space in which computational methods need to be used.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.000 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.002 |
| 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".