Markovian properties of passive scalar increments in grid-generated turbulence
Bibliographic record
Abstract
Recent research (Renner, Peinke and Friedrich 2001 J. Fluid Mech. 433 383) has shown that the statistics of velocity increments in a turbulent jet exhibit Markovian properties for scales of size greater than the Taylor microscale, λ. In addition, it was shown that the probability density functions (PDFs) of the velocity increments, v (r), were governed by a Fokker–Planck equation. Such properties for passive scalar increments have never been tested. The present work studies the (velocity and) temperature field in grid-generated wind tunnel turbulence for Taylor-microscale-based Reynolds numbers in the range 140⩽Rλ⩽582. Increments of longitudinal velocity were found to (i) exhibit Markovian properties for separations r⪆λ and (ii) be describable by a Fokker–Planck equation because terms in the Kramers–Moyal expansion of order >2 were small. Although the passive scalar increments, δ(r), also exhibited Markovian properties for a similar range of scales as the velocity field, the higher-order terms in the Kramers–Moyal expansion were found to be non-negligible at all Reynolds numbers, thus precluding the PDFs of δ(r) from being described by a Fokker–Planck equation. Such a result indicates that the scalar field is less Markovian than the velocity field—an attribute presumably related to the higher level of internal intermittency associated with passive scalars.
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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".