Numerical challenges for turbulence computation: statistical equipartition and the method of spectral reduction
Bibliographic record
Abstract
Numerical issues in the implementation of spectral reduction, a new method for the computation of statistical moments of homogeneous turbulence, are examined. The method implements a coarse graining in Fourier space and exploits the fact that statistical moments are much smoother functions of wave number than the underlying fluctuating velocities. A notable feature of this turbulence model is the existence of a control parameter (bin size) that can be varied to increase the accuracy of the approximation. The inviscid version of spectral reduction satisfies a Liouville theorem and yields statistical equipartition solutions. However, if the wavenumber bins are of nonuniform size (as is desirable for efficiency), an additional bin-dependent rescaling of time by the relative bin area must be introduced to obtain the correct equipartition. This rescaling of the time derivative term drastically increases the stiffness of the spectrally reduced equations. The prospect of developing an implicit nonlinear integrator for this highly stiffened convection problem is examined.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.004 | 0.003 |
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".