Revisiting the quest for a universal log-law and the role of pressure gradient in "canonical" wall-bounded turbulent flows
Bibliographic record
Abstract
The trinity of so-called "canonical" wall-bounded turbulent flows, comprising the zero pressure gradient turbulent boundary layer, abbreviated ZPG TBL, turbulent pipe flow and channel/duct flows has continued to receive intense attention as new and more reliable experimental data have become available. Nevertheless, the debate on whether the logarithmic part of the mean velocity profile, in particular the Kármán constant $κ$, is identical for these three canonical flows or flow-dependent is still ongoing. In this paper, which expands upon Monkewitz and Nagib (24th ICTAM Conf., Montreal, 2016), the asymptotic matching requirement of equal $κ$ in the log-law and in the expression for the centerline/free-stream velocity is reiterated and shown to preclude a single universal log-law in the three canonical flows or at least make it very unlikely. The current re-analysis of high quality mean velocity profiles in ZPG TBL's, the Princeton "Superpipe" and in channels and ducts leads to a coherent description of (almost) all seemingly contradictory data interpretations in terms of TWO logarithmic regions in pipes and channels: A universal interior, near-wall logarithmic region with the same parameters as in the ZPG TBL, in particular $κ_{\mathrm{wall}} \cong 0.384$, but only extending from around $150$ to around $10^3$ wall units, and shrinking with increasing pressure gradient, followed by an exterior logarithmic region with a flow specific $κ$ matching the logarithmic slope of the respective free-stream or centerline velocity. The log-law parameters of the exterior logarithmic region in channels and pipes are shown to depend monotonically on the pressure gradient.
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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 | 0.002 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.009 |
| Scholarly communication | 0.004 | 0.009 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".