Vortex Structure and Instability Characteristics of Dean–Taylor Flow through a Rotating Bent Square-Shaped Enclosure
Bibliographic record
Abstract
The present paper investigates solution structure, instability characteristics, and chaotic nature of the Dean–Taylor flow with energy distribution through a rotating bent square-shaped enclosure adopting a spectral-based numerical approach. The channel is rotated about the vertical axis in the positive direction for the Taylor number $$0 \leqslant {\text{Tr}} \leqslant 2000$$ . A temperature difference is applied across the vertical walls while a room temperature is maintained on the horizontal walls. Numerical calculations are carried out for the Dean number $${\text{Dn}} = 1000$$ over a wide of curvature ranging from 0.001 to 0.5, and the combined effects of centrifugal, Coriolis, and buoyancy forces are examined. As a result, three branches of asymmetric steady solutions (SS), composed of 2- to 4-vortex solutions, are obtained by using arc-length path continuation technique. To understand the unsteady nature, the transient solution is then inspected by time series analysis, and flow transition is precisely identified by determining the phase trajectory of the temporal development and assessing the power spectrum density. The study shows that, as Tr increases, the flow progresses through various instabilities namely multi-periodic, chaotic, steady-state, periodic, and then chaotic-state again, demonstrating a transition that features asymmetric 2- to 8-vortex solutions. Nusselt numbers are calculated as a measure of convective heat transfer (HT) between the heating wall and the fluid, and it is discovered that chaotic flow (SF) considerably improves convective heat transfer (CHT). Finally, our computational findings are assessed against previously reported experimental data, and an adequate consistency is observed.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| 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 source (direct Gemma or distilled Codex), 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".