Linear analysis of the stability of particle-laden stratified shear layers
Bibliographic record
Abstract
Hydrodynamic instabilities at the interface of stratified shear layers could occur in various modes and have an important role in the mixing process. In this work, the linear stability analysis in the temporal framework is used to study the stability characteristics of a particle-laden stratified two-layer flow for two different background density profiles: smooth (hyperbolic tangent) and piecewise linear. The effect of parameters, such as bed slope, viscosity, and particle size, on the stability is also considered. The pseudospectral collocation method employing Chebyshev polynomials is used to solve two coupled eigenvalue equations. Based on the results, there are some differences in the stability characteristics of the two density profiles. In the case of R = 1 (R is the ratio of the shear layer thickness to the density layer thickness), the stability boundary in smooth profile is the transition from the unstable flow (where the dominant unstable mode is Kelvin–Helmholtz) to the stable one where in the piecewise linear profile this boundary is the transition from Kelvin–Helmholtz to the Holmboe mode. It is also shown that the unstable region increases with the bed slope and unstable modes amplify as the bed slope increases. For R = 5 the flow does not become stable by increasing the stratification in nonzero bed slope, and in some wavenumbers the Kelvin–Helmholtz and Holmboe modes coexist. In addition, by increasing the bed slope the growth rate of the Holmboe mode and the range of its existence decrease. As expected, the viscosity makes the current more stable, and for large values of the viscosity (small Reynolds number) the flow becomes stable at long waves (small wave numbers) for all bulk Richardson numbers. Existence of small particles does not change the instability characteristics so much, however, large particles make the flow more unstable.
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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 | 0.001 |
| 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".