The three effects of the pressure force on turbulent boundary layers
Bibliographic record
Abstract
This study aims to isolate the three effects of the pressure force on the inner and outer layers: the local direct impact (characterized by the pressure gradient parameter, β ), the local disequilibrating effect (represented here by the normalized streamwise derivative d β / d X ), and the upstream cumulative effect, while also accounting for the inevitable Reynolds number influence. To achieve this objective, we draw on several non-equilibrium and near-equilibrium databases from the literature, and employ a methodology based on the selection of pressure-gradient parameters — distinct for the inner and outer layers — that capture the local direct impact and the local disequilibration effect of the pressure gradient. The pressure force impact on the inner and outer regions is represented by two parameters: the friction–viscous pressure-gradient parameter, β i , and the pressure-gradient parameter based on Zagarola–Smits velocity, β Z S , respectively. In the non-equilibrium flow cases, both β i and β Z S exhibit similar distributions, initially increasing and then decreasing. However, the rate of change of these parameters along the streamwise direction varies among the flows, indicating differing levels of pressure force disequilibration. In addition, we employ two near-equilibrium cases with minimal variations of the pressure gradient parameters for comparisons. In the outer layer, it is found that both the local and cumulative disequilibrating effects modify the mean velocity and Reynolds stress profiles at identical β Z S values. The faster the variations in pressure force impact, the more delayed the response of both mean flow and turbulence. Cumulative effects prove to be significant. In the inner layer, which responds much faster to changes in pressure force, the local disequilibrating effect still modifies the mean velocity profile in the viscous sublayer. Notably, when the mean velocity defect is significant, the behavior of u -structures in the inner layer appears to be governed by how outer turbulence responds to pressure force effects. In contrast, the size of u v -structures in the inner layer scales with the mixed pressure-friction length ( ν / u τ + ν / u p i ) . Unlike inner u -structures, they are independent of large-scale outer structures and flow history. • Pressure force variations alter the flow even when the force balance is similar. • Rapid pressure force variations further delay the flow response. • Flow history has minimal effect on inner velocity, regardless of pressure force. • Inner-layer u v -structures size scales with a mixed friction–pressure length scale.
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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".