The continuous spectrum for a boundary layer in a streamwise pressure gradient
Bibliographic record
Abstract
Solutions of the Orr–Sommerfeld equation belonging to the continuous spectrum are presented for boundary layers developing in the presence of a streamwise pressure gradient. Although the continuous spectrum has received considerable attention in the Blasius case, in most engineering applications transition to turbulence occurs in a region where there is a pressure gradient. This investigation, so far as we know, is the first to examine what effect this has on the eigenfunctions. Our results show that when there is a pressure gradient the magnitude of the eigenfunctions near the edge of the boundary layer can be much larger than it is for Blasius flow. This is particularly true when the pressure gradient is adverse, but such is the case even when it is favorable. We also investigate the effect of Reynolds number and frequency on the penetration depth; the latter term refers to one of the properties of these modes that distinguishes them from Tollmien–Schlichting waves, namely, that their magnitude is largest near the edge of the boundary layer, but much smaller inside.
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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".