Influence of inertia on the transient axisymmetric free-surface flow inside thin cavities of arbitrary shape
Bibliographic record
Abstract
The influence of inertia is examined for transient axisymmetric free surface flow inside a thin cavity of arbitrary shape. The flow field is obtained by solving the lubrication equations, which are averaged over the cavity gap by expanding the velocity in terms of Chandrasekhar functions and using the Galerkin projection method. The formulation accounts for the transverse flow, as well as nonlinearities stemming from inertia and front location. Both flows under an imposed flow rate, and an imposed pressure at the cavity entrance are examined. The influence of inertia, aspect ratio, gravity, and cavity geometry on the evolution of the front, flow rate, and pressure is assessed particularly in the early stage of flow. Comparison with existing results shows full qualitative agreement for cavities of various geometries and flow conditions. Inertia is found to have a significant influence on early transient behavior, leading to the development of a flow of the “boundary-layer” type upon inception. The effect of inertia is further explored by developing a multiple-scale analysis to obtain an approximate solution at small Reynolds number, Re. Comparison with the exact (numerical) solution indicates a wide range of validity for the multiple-scale approach, even in the moderately small Re range.
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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 | 0.001 |
| 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".