The stochastic mode of the Faraday instability of shallow fluid layers
Bibliographic record
Abstract
The instability of a vertically oscillated layer of fluid is a classical problem whose history dates back to Faraday in the 19th century. We consider the stability of a shallow layer for which the oscillation, as expressed through the effective gravitational acceleration, is a random function of time. Using both theoretical linear stability analysis and high-resolution numerical simulations, including both individual realizations and ensemble calculations, of the nonlinear system of equations, we find that two different stochastic modes of instability exist. Both modes find their expression in finite amplitude oscillations of the free surface that exhibit sharp crests and broad troughs, or in other words, that resemble the classical Stokes wave. We demonstrate that a necessary condition for the first type of instability is snapshot, or instantaneous, instability. The subdominant instability resembles classical parametric resonance that can exist in a harmonically oscillated layer of fluid, and occurs even when the flow is always snapshot stable (or the gravitational acceleration is non-negative).
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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) | 0.000 | 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".