Pump Flow Solutions of the Navier–Stokes Equations
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Bibliographic record
Abstract
Exact solutions of the Navier–Stokes equations are used to describe pump flows that involve the interaction of several different components. As an illustration of the general representations obtained, a detailed description is given of flows that involve both a swirl and a shear component. Such flows are common in the atmosphere. For example, they are produced in the core of a vortex as it moves over a horizontal surface into a region where the flow is sheared in a direction normal to the surface. Far from the surface, the vortex core translates in a direction parallel to the surface, and the flow asymptotes to that in an Ekman spiral. When the core rotates and translates with speeds that vary in time, the flow develops both updraft and downdraft regions.
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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 it