The effect of Prandtl number on mixing in low Reynolds number Kelvin-Helmholtz billows
Bibliographic record
Abstract
The effect of Prandtl number on mixing in temporally evolving Kelvin-Helmholtz (KH) instabilities at low to moderate Reynolds numbers is studied through direct numerical simulation. We distinguish between the mixing induced by the primary billow and the mixing generated by three-dimensional motions by performing each simulation in two and three dimensions. The results indicate that the time evolution of the rate of two- and three-dimensional mixing through different stages of the life cycle of KH flow is significantly influenced by the Prandtl number. As the Prandtl number increases, the final amount of mixing increases for Reynolds that are too low to support active three-dimensional motions. This trend is the opposite in sufficiently high Reynolds number KH flows that can overcome viscous effects and develop significant three-dimensional instabilities. While the mixing generated in the two-dimensional flows, uniform in the span-wise direction, is not significantly dependent on the Prandtl number, the turbulent mixing induced by three-dimensional motions is a function of the Prandtl number. We observe a steady increase in the total amount of mixing for buoyancy Reynolds numbers above 7, consistent with the results of Shih et al. [“Parameterization of turbulent fluxes and scales using homogeneous sheared stably stratified turbulence simulations,” J. Fluid Mech. 525, 193-214 (2005)]. Both maximum instantaneous and cumulative mixing efficiencies exhibit a decreasing trend with increasing Prandtl number. We compare the dependence of the mixing efficiency on Prandtl number to previous studies.
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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
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