An Extended Rayleigh Equation for the Uniform Inviscid Plane Flow with Gas Bubble Crossflow
Bibliographic record
Abstract
The classic second-order Rayleigh equation governs the linear stability of single-phase inviscid plane flows, and its extension to two-phase inviscid plane flows with a crossflow of another fluid remains to be investigated. The present work studies the linear stability of steady uniform inviscid two-phase flow in a horizontal channel with gas bubbles injected from the lower wall and removed from the upper wall. An extended fourth-order Rayleigh equation with constant coefficients is derived for the linear stability of the two-phase uniform inviscid plane flow with the bubble crossflow injected at the bubble terminal velocity. Our analytical results show that the uniform inviscid plane flow driven by the bubble crossflow is linearly unstable with rapidly growing disturbances in the absence of the lift force. On the other hand, when the positive lift force coefficient is nearly equal to the added mass coefficient, the uniform inviscid plane flow driven by the bubble crossflow is linearly stable to the admissible disturbances consistent with the bubble-injection boundary conditions. These analytical results reveal the destabilizing effect of the bubble crossflow and confirm the stabilizing effect of the positive lift force on the inviscid plane flows, which could stimulate further research interest in the qualitatively different roles of the bubble crossflow and the lift force in the stability of inviscid plane flows as compared to viscous plane flows.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".