Loss of monotonicity and anomalous scaling behavior in the passive scalar gradient
Bibliographic record
Abstract
Purpose The purpose of this paper is to discuss some fundamental aspects regarding the anomalies in the passive scalar field advected by forced homogenous and isotropic turbulence, by inspection of the analytical properties of the governing equations and with the aid of direct numerical simulation (DNS) data. Design/methodology/approach Results from a pseudo‐spectral DNS of a unitary‐Schmidt‐ number passive scalar advected by a low Reynolds number flow field, Re λ =50 and 70 (based on the Taylor microscale λ ) allow for a preliminary assessment of the developed numerical model. Findings Manipulation of the governing equations for the scalar field (which are monotonic) reveals that the unboundedness of the scalar gradient magnitude is not ruled out by the mathematical properties of the correspondent conservation equation. Classic intermittency effects in the passive scalar field have been reproduced, such as non‐Gaussian behavior of the passive scalar statistics, loss of local isotropy, and multi‐fractal scaling of scalar structure functions. Moreover, Taylor and Richardson theories are, surprisingly, not confirmed only in the dissipation range (small‐scales anomalies). Originality/value The authors suggest that the origin of intermittency (qualitatively pictured here as violent burst in spatial gradient quantities) should be sought in the loss of monotonicity of the evolution equation of the scalar gradient.
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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 | 0.001 | 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".