Wavenumber lock-in and spatial parametric resonance in convection
Bibliographic record
Abstract
Analysis of convection driven by spatial periodic heating shows a wealth of responses due to Prandtl number dependence. The primary convection is delineated by the heating wavenumber and the secondary convection is characterized by the critical wavenumber established by an instability process. The resulting two-wavenumber dynamical system involves spatial parametric resonance leading to the wavenumber lock-in and the Rayleigh–Bénard (RB) instability producing unlocked states. Heating conditions leading to the co-existence of both types of states have been identified. Transition from the locked to the unlocked states produces states with a wide range of wavelengths and diverse patterns of movement. The possible secondary states are driven by a competition between the RB mechanism and the spatial parametric resonance. The relative strengths of these mechanisms change with Prandtl number $Pr$ resulting in four types of system responses. In the type A response occurring for $Pr>0.4$ , parametric resonance dominates for the heating wavenumber $\alpha < 4.5$ resulting in the pattern lock-in between the primary and secondary convections whereas RB occurs for $\alpha > 10$ . There is a wealth of possible convection patterns in the in-between zone where a small change of $\alpha$ results in a major change of flow pattern. In the type B response, which occurs for $0.19< Pr< 0.4$ , the RB effect dominates eliminating the lock-in. The type C response, which occurs for $0.08 < Pr< 0.19$ , is similar to type A but stronger spatial modulation extends the range of dominance of parametric resonance up to $\alpha =7$ while the RB effect dominates for $\alpha >10$ as in the type A response. A wealth of possible patterns occurs in the transition zone ( $7<\alpha <10$ ). In the type D response, which occurs for $Pr<0.08$ , the strong spatial modulation results in the formation of two separate critical stability curves, one resulting from the dominance of the spatial parametric resonance leading to the lock-in effect, and the other one corresponding to the dominance of the RB effect producing unlocked states. No continuous transition between both states can occur. Conditions where both distinct states can arise simultaneously were identified. Morphing between different patterns of secondary convection may occur in response to small changes in the heating pattern in types A and C, while such processes are not possible in types B and D.
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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 | 0.001 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".