Velocity perturbations and Reynolds stresses in Holmboe instabilities
Bibliographic record
Abstract
The velocity perturbations and Reynolds stresses associated with finite-amplitude Holmboe instabilities are investigated using linear stability analysis, numerical simulations, and laboratory experiments. The rightward and leftward propagating Holmboe instabilities are separated, allowing for a direct comparison of the perturbation fields between the numerical simulations and the linear stability analysis. The decomposition and superposition of the perturbation fields provide insights into the structure and origin of Reynolds stresses in Holmboe instabilities. Shear instabilities in stratified flows introduce a directional preference (anisotropy) in velocity perturbation fields, thereby generating Reynolds stresses. Here, we investigate this anisotropy by comparing pairs of horizontal and vertical velocity perturbations (u′,w′), obtained from the simulations and the laboratory experiment, with predictions from linear stability analysis. For an individual Holmboe mode, both the simulations and linear theory yield elliptical (u′,w′)-pairs that are oriented toward the second and fourth quadrants (u′w′<0), corresponding to the tilted elliptical trajectories of particle movement. Combining the leftward and rightward Holmboe modes yields (u′,w′) ellipses whose orientation and aspect ratio are phase-dependent. When averaged over a full cycle, the joint probability density functions of (u′,w′) in the linear theory and single wavelength simulations exhibit “steering wheel” structures. This steering wheel is smeared out in multiple wavelength simulations and the laboratory experiment due to varying wavelengths, resulting in an elliptical cloud. All of the approaches adopted in the present study yield Reynolds stresses that are comparable to those reported in previous laboratory and field investigations.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".