New similarity reductions and exact solutions for helically symmetric viscous flows
Bibliographic record
Abstract
In the present paper, we derive exact solutions for the helically invariant Navier–Stokes equations. The approach is based on an invariant solution ansatz emerging from the Galilean group in helical coordinates, which leads to linear functions in the helical coordinate ξ = az + bφ for the two helical velocity components uξ and uη. The variables z and φ are the usual cylinder coordinates. Starting from this approach, we derive a new equation for the radial velocity component ur in the helical frame, for which we found two special solutions. Moreover, we present an exact linearization of the Navier–Stokes equations by seeking exact solutions in the form of Beltrami flows. Using separation of variables, we found exponentially decaying time-dependent solutions, which consist of trigonometric functions in the helical coordinate ξ and of confluent Heun-type functions in the radial direction.
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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".