Scaling of space–time modes with Reynolds number in two-dimensional turbulence
Bibliographic record
Abstract
It has been estimated that the number of spatial modes (or nodal values) required to uniquely determine a two-dimensional turbulent flow at a specific time is finite, and is bounded by Re4/3 for forced turbulence and Re for decaying turbulence. The usual computational estimate of the number of space–time modes required to calculated decaying two-dimensional turbulence is ${\cal N}\sim{Re}^{3/2}$ . These bounds neglect intermittency, and it is not known how sharp they are. In this paper we use an adaptive multi-scale wavelet collocation method to estimate for the first time the number of space–time computational modes ${\cal N}$ necessary to represent two-dimensional decaying turbulence as a function of Reynolds number. We find that ${\cal N}\sim{Re}^{0.9}$ for 1260 ≤ Re ≤ 40400 over many eddy turn-over times, and that temporal intermittency is stronger than spatial intermittency. The spatial modes alone scale like Re0.7. The β-model then implies that the spatial fractal dimension of the active regions is 1.2, and the temporal fractal dimension is 0.3. These results suggest that the usual estimates are not sharp for adaptive numerical simulations. The relatively high compression confirms the importance of intermittency and encourages the search for reduced mathematical models of two-dimensional turbulence (e.g. in terms of coherent vortices).
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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 | 0.000 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".