Invariants for slightly heated decaying grid turbulence
Bibliographic record
Abstract
Abstract The paper examines the validity of velocity and scalar invariants in slightly heated and approximately isotropic turbulence generated by passive conventional grids. By assuming that the variances $\langle {u}^{2} \rangle $ and $\langle {\theta }^{2} \rangle $ ( $u$ and $\theta $ represent the longitudinal velocity and temperature fluctuations) decay along the streamwise direction $x$ according to power laws $\langle {u}^{2} \rangle \sim {(x- {x}_{0} )}^{{n}_{u} } $ and $\langle {\theta }^{2} \rangle \sim {(x- {x}_{0} )}^{{n}_{\theta } } $ ( ${x}_{0} $ is the virtual origin of the flow) and with the further assumption that the one-point energy and scalar variance budgets are represented closely by a balance between the rates of change of $\langle {u}^{2} \rangle $ and $\langle {\theta }^{2} \rangle $ and the corresponding mean energy dissipation rates, the products $\langle {u}^{2} \rangle { \lambda }_{u}^{- 2{n}_{u} } $ and $\langle {\theta }^{2} \rangle { \lambda }_{\theta }^{- 2{n}_{\theta } } $ must remain constant with respect to $x$ . Here ${\lambda }_{u} $ and ${\lambda }_{\theta } $ are the Taylor and Corrsin microscales. This is unambiguously supported by previously available data, as well as new measurements of $u$ and $\theta $ made at small Reynolds numbers downstream of three different biplane grids. Implications for invariants based on measured integral length scales of $u$ and $\theta $ are also tested after confirming that the dimensionless energy and scalar variance dissipation rate parameters are approximately constant with $x$ . Since the magnitudes of ${n}_{u} $ and ${n}_{\theta } $ vary from grid to grid and may also depend on the Reynolds number, the Saffman and Corrsin invariants which correspond to a value of $- 1. 2$ for ${n}_{u} $ and ${n}_{\theta } $ are unlikely to apply in general. The effect of the Reynolds number on ${n}_{u} $ is discussed in the context of published data for both passive and active grids.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| 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 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".