Conditional statistics for a passive scalar with a mean gradient and intermittency
Bibliographic record
Abstract
The conditional dissipation and diffusion for a passive scalar with an imposed mean gradient are studied here. The results are obtained for an elementary model consisting of a random shear flow with a simple time-periodic transverse sweep. As the Peclet number is increased, scalar intermittency is observed; the scalar probability density function departs strongly from a Gaussian law. As a result, the conditional dissipation undergoes a transition from a quadratic behavior for the near-Gaussian probability distribution case at low Peclet number to a more complex shape at large Peclet. The conditional diffusion also undergoes a transition, this time from a linear to a nonlinear dependence, for cases with sufficient intermittency as well as a significant contribution from multiple spatial modes. The present analysis sheds some light on similar behaviors observed recently in numerical simulations of more complex models. The statistics in the present study are obtained by exact processing of one-dimensional quadrature results so that all sampling errors are eliminated, including in the tails of the distribution. This allows for a quantification of typical sampling errors when the conditional statistics are processed from numerical databases. The robustness of models based on polynomial fits for the conditional statistics is also assessed.
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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".