Application of power laws to low Reynolds number boundary layers on smooth and rough surfaces
Bibliographic record
Abstract
Scaling laws for the overlap region of near-wall turbulent flows are of particular interest to turbulence researchers and engineers. For the mean flow at sufficiently high Reynolds numbers, the classical boundary layer theory proposes a logarithmic law for the overlap region. On the other hand, at low Reynolds numbers, refined measurements and direct numerical simulation results indicate that the log law region becomes negligibly small. Instead, power laws have received increasing attention as an alternative formulation for the overlap region at low Reynolds numbers. In the present study, we use open channel flow measurements to assess the ability of the power laws proposed by Barenblatt [J. Fluid Mech. 248, 513 (1993)] and George and Castillo [Appl. Mech. Rev. 50, 689 (1997)] to describe the overlap region in low Reynolds number boundary layers on smooth and rough surfaces. The skin friction laws derived from the power laws are also used to estimate the friction velocity, which values are then compared to measurements obtained by other reliable techniques. The results indicate that at low Reynolds numbers the power law formulations can model a wider extent of the flow than the classical logarithmic profile. Both Barenblatt’s and George and Castillo’s power laws give an excellent prediction of the friction velocities for flows over a smooth surface, but only the skin friction law proposed by George and Castillo gives good prediction for the rough wall data.
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 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".