Asymptotic solutions for shocked resonant acoustic oscillations between concentric spheres and coaxial cylinders
Bibliographic record
Abstract
For resonant oscillations of a gas in a straight tube with a closed end, shocks form and all harmonics are generated, see Chester [“Resonant oscillations in a closed tube,” J. Fluid Mech. 18, 44 (1964)]10.1017/S0022112064000040. When the gas is confined between two concentric spheres or coaxial cylinders, the radially symmetric resonant oscillations may be continuous or shocked. For a fixed small Mach number of the input, the flow is continuous for sufficiently small L, defined as the ratio of the inner radius to the difference of the radii, see Seymour et al. [“Resonant oscillations of an inhomogeneous gas between concentric spheres,” Proc. R. Soc. London, Ser. A 467, 2149 (2011)]10.1098/rspa.2010.0576. However, shocks appear in the resonant flow for either larger values of L or larger input Mach number. A nonlinear geometric acoustics approximation is used to analyse the shocked motion of the gas when L ≫ 1. This approximation and the exact numerical solution are compared for the shocked wave profiles and shock strengths, and the approximation is valid for surprisingly small values of L. The flow in the plane wave case for a straight tube is recovered in the limit L → ∞ for both the spherical and cylindrical cases, providing a check on the results. The shocked solutions given here complement those continuous solutions previously derived from a dominant first mode approximation.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".