The disturbance energy and Rayleigh criterion in a non-ideal compressible fluid
Bibliographic record
Abstract
Small perturbation theory neglects non-linear terms and allows for analytical predictions and identifications of physical trends. It can then be used for the understanding and modelling of more complicated nonlinear phenomena, e.g. turbulence and fluid instabilities. In compressible fluids these theories generally rely on the ideal gas assumption. This article theoretically examines the fluctuations in a non-ideal compressible fluid, utilising the Navier–Stokes-Fourier model, with an arbitrary equation of state. The linearised governing system is deduced, thereafter elucidating the amplification or attenuation of fluctuations through an analysis of energy disturbance, extending the framework established by Chu (Chu, 1965) to encompass arbitrary non-ideal compressible fluids. It is demonstrated that the proposed disturbance energy embodies the same advantageous properties as Chu’s ideal-gas one. The study of the time evolution of the disturbance energy then allows to derive a simple stability criteria generalising the Rayleigh criterion (Rayleigh, 1878) to steady and non-uniform flows of non-ideal compressible fluids. Similar to the Rayleigh criterion, this criterion offers novel physical insights into the amplification or attenuation of arbitrary fluctuations within non-ideal compressible fluids. Moreover, the present work represents an advancement attempting to extend classical findings derived under the ideal gas assumption to integrate alternative equations of state. The analysis and equations derived are expected to allow improvements in both the understanding and modelling of disturbances in non-ideal compressible fluids. • Rayleigh stability criterion can be generalized to arbitrary fluids. • A new criterion is analytically derived from Navier–Stokes–Fourier. • It is valid for arbitrary non-ideal compressible fluids. • It is a simple tool to assess the stability of flows of non-ideal fluids. • It generalizes Chu’s energy to arbitrary fluids and shares its appealing mathematical properties.
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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".