Linear stability of a Berman flow in a channel partially filled with a porous medium
Bibliographic record
Abstract
The temporal stability of similarity solutions for an incompressible fluid moving in a channel partially filled with a porous medium is analyzed. A constant wall suction acting on the bottom surface of the porous medium drives the fluid; the upper wall of the channel is impermeable. This work extends the work of King and Cox [“Asymptotic analysis of the steady-state and time-dependent Berman problem,” J. Eng. Math. 39, 87 (2001)] to a wider class of similarity solutions where coupled flow, both above and through a porous medium, is considered. In this work, a similarity transform is proposed which satisfies both the Navier–Stokes equation in the clear fluid portion of the domain and the Brinkman extended Darcy law relationship in the porous medium. The boundary conditions between the clear fluid and porous regions are those outlined by Ochoa-Tapia and Whitaker [“Momentum transfer at the boundary between a porous medium and a homogeneous fluid I: theoretical development,” Int. J. Heat Mass Transfer 38, 2635 (1995)]. The solutions of the steady flow are approximated analytically, in the limit of small wall suction, and numerically. Multiple steady-state solutions were found. The temporal stability of the solutions indicates turning-point bifurcations and instability only occurred with reverse flows.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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".