A conceptual generalization of Taylor microscales with applications to isotropic and wall turbulence
Bibliographic record
Abstract
Two new concepts of the Taylor microscale matrix (TMM) and Taylor microscale tensor (TMT) are proposed to extend the classical concept of Taylor microscale of isotropic turbulence to the general scenario of anisotropic turbulence. The first concept TMM is derived from the classical definition of two-point auto-correlation function, which has shortcomings for not being a tensor. The second concept TMT is proposed based on a new correlation function that rigorously maintains tensor properties. The three eigenvalues of TMM or TMT represent the general Taylor microscales (GTMs). When these three new general concepts, TMM, TMT, and GTM, are applied to homogeneous and isotropic turbulence, the classical Taylor microscale is automatically recovered. The proposed concepts can also be used for characterizing anisotropic turbulence. To demonstrate, direct numerical simulations (DNSs) of turbulent plane-channel flows of three Reynolds numbers are performed. The asymptotic near-wall behaviors of GTM are derived analytically and validated using DNS data. In the current literature, it is popular to study the orientation of turbulent flow structures qualitatively based on the isopleths of a two-point auto-correlation function. As a new advancement, a rigorous explanation of this popular approach is obtained based on the concept of GTM such that the characteristic inclination angle of flow structures (such as the mean angle of hairpin packets) can be precisely defined and computed. It is interesting to observe that in the outer layer, the mean streamwise spacing between two successive hairpin vortices in a hairpin packet is approximately twice the proposed GTM λT1(1).
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| 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 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".