Infrared Dynamics of Decaying Two-Dimensional Turbulence Governed by the Charney-Hasegawa-Mima Equation
Bibliographic record
Abstract
The low wave number range of decaying turbulence governed by the Charney-Hasegawa-Mima (CHM) equation is examined theoretically and by direct numerical simulation. Here, the low wave number range is defined as values of the wave number k below the wave number k E corresponding to the peak of the energy spectrum, or alternatively the centroid wave number of the energy spectrum. The energy spectrum in the low wave number range in the infrared regime ( k →0) is theoretically derived to be E ( k ) ∼ k 5 , using a quasinormal Markovianized model of the CHM equation. This result is verified by direct numerical simulation of the CHM equation. The wave number triads ( k , p , q ) responsible for the formation of the low wave number spectrum are also examined. It is found that the energy flux Π( k ) for k < k E can be entirely expressed by Π (-) ( k ), which is the total net input of energy to wave numbers < k arising from interactions with wave numbers p , q > k . Furthermore, the contribution of nonlocal triad interactions to the energy flux is found to be predominant in the range log ( k / k E )<-0.5, where the nonlocal interactions are defined to be those triad interactions for which the ratio of the largest leg of the triad to the smallest leg is larger than four.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 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".