Roll waves on laminar sheet flow of Newtonian fluid with negligible surface tension
Bibliographic record
Abstract
We conduct direct numerical simulations (DNS) to study the temporal and spatial developments of the roll waves on a laminar sheet flow of Newtonian fluid. The DNS unveil the physics of the wavefront and show the limitation of the widely used shallow-layer approximations. The most prominent wave, the front runner, is determined by the DNS for the first time in studying the spatial development of the laminar sheet flow with negligible surface tension. Depending on the Froude and Reynolds numbers, the front runner can be a multi-peaked undular bore or a single-peaked non-breaking or breaking wave. The simulation has uncovered an extended region behind the wavefront, where the bed-friction stress is much higher than the corresponding friction in the undisturbed uniform flow. It also produces an uplift velocity needed in the description of wave breaking. For comparison, we also examine the nonlinear development of the instability using two-equation and four-equation shallow-layer models. The two-equation shallow-layer model has produced the bulk of the wave profile but is deficient because it fails to predict the uplift velocity and the substantial increase in bed friction in the frontal region. The four-equation shallow-layer model correctly predicts the bed friction but cannot produce the breaking wave. The simulations also determine the celerity and amplitude of the front runner to follow a linear relationship, qualitatively similar to the roll waves in a turbulent flow.
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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".