On new stability modes of plane canonical shear flows using symmetry classification
Bibliographic record
Abstract
In the work of Nold and Oberlack [Phys. Fluids 25, 104101 (2013)], it was shown that three different instability modes of the linear stability analysis perturbing a linear shear flow can be derived in the common framework of Lie symmetry methods. These modes include the normal-mode, the Kelvin mode, and a new mode not reported before. As this was limited to linear shear, we now present a full symmetry classification for the linearised Navier-Stokes equations which are employed to study the stability of an arbitrary plane shear flow. If viscous effects for the perturbations are neglected, then we obtain additional symmetries and new Ansatz functions for a linear, an algebraic, an exponential, and a logarithmic base shear flow. If viscous effects are included in the formulation, then the linear and a quotient-type base flow allow for additional symmetries. The symmetry invariant solutions derived from the new and classical generic symmetries for all different flow types naturally lead to algebraic growth and decay for all cases except for two linear base flow cases. In turn this leads to the formulation of a novel eigenvalue problem in the analysis of the transition to turbulence for the respective flows, all of which are very distinct from the classical Orr-Sommerfeld eigenvalue problems.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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".