Onset of turbulence and layering in stratified columnar Taylor–Green vortices
Bibliographic record
Abstract
We use direct numerical simulations to examine the onset of stratified turbulence triggered by the zigzag instability recently identified in columnar Taylor–Green vortices (Guo etal. 2024, J. Fluid Mech., vol. 997, A34) and its role in layer formation within the flow. The study focuses on Froude numbers $0.125 \leqslant \textit{Fr} \leqslant 2.0$ and Reynolds numbers ${\textit{Re}}$ ranging from 800 to 3200. The breakdown of the freely evolving vortex array is driven by local density overturns, combining shear and convective mechanisms initiated by the primary zigzag instability. Our results show a linear relationship between the peak buoyancy Reynolds number ${{\textit{Re}}}_b^{\star }$ , driven by the zigzag instability, and ${\textit{Re}}\, {\textit{Fr}}^2$ . When the flow does not exhibit local shear or convective instability, the value of ${{\textit{Re}}}_b^{\star }$ falls below unity. Both density and momentum layers arise from the zigzag instability: horizontal velocity layers are strong and persistent, while density layers are weaker and more transient. The vertical scale of the mean shear layers increases with ${\textit{Fr}}$ for ${\textit{Fr}} \leqslant 1$ , shows weak dependence on ${\textit{Re}}$ , and agrees well with the length scale associated with the fastest-growing linear mode of the zigzag instability. Further analysis in the sorted buoyancy coordinate highlights the role of density overturns caused by the zigzag instability in forming buoyancy layers during the transition to turbulence.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.000 |
| 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".