Impact of the inherent separation of scales in the Navier–Stokes-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>α</mml:mi><mml:mi>β</mml:mi></mml:mrow></mml:math>equations
Bibliographic record
Abstract
We study the effect of the length scales $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ in the Navier--Stokes-$\ensuremath{\alpha}\ensuremath{\beta}$ equations on the energy spectrum and the alignment between the vorticity and the eigenvectors of the stretching tensor in three-dimensional homogeneous and isotropic turbulent flows in a periodic cubic domain, including the limiting cases of the Navier--Stokes-$\ensuremath{\alpha}$ and Navier--Stokes equations. A significant increase in the accuracy of the energy spectrum at large wave numbers arises for $\ensuremath{\beta}<\ensuremath{\alpha}$. The vorticity structures predicted by the Navier--Stokes-$\ensuremath{\alpha}\ensuremath{\beta}$ equations also improve as $\ensuremath{\beta}$ decreases away from $\ensuremath{\alpha}$. However, optimal choices for $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ depend not only on the problem of interest but also on the grid resolution.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".