ENERGY CONSERVATION AND GRAVITY WAVES IN SOUND-PROOF TREATMENTS OF STELLAR INTERIORS. II. LAGRANGIAN CONSTRAINED ANALYSIS
Bibliographic record
Abstract
The speed of sound greatly exceeds typical flow velocities in many stellar and planetary interiors.To follow the slow evolution of subsonic motions, various sound-proof models attempt to remove fast acoustic waves while retaining stratified convection and buoyancy dynamics.In astrophysics, anelastic models typically receive the most attention in the class of sound-filtered stratified models.Generally, anelastic models remain valid in nearly adiabatically stratified regions like stellar convection zones, but may break down in strongly sub-adiabatic, stably stratified layers common in stellar radiative zones.However, studying stellar rotation, circulation, and dynamos requires understanding the complex coupling between convection and radiative zones, and this requires robust equations valid in both regimes.Here we extend the analysis of equation sets begun in Brown et al., which studied anelastic models, to two types of pseudo-incompressible models.This class of models has received attention in atmospheric applications, and more recently in studies of white-dwarf supernova progenitors.We demonstrate that one model conserves energy but the other does not.We use Lagrangian variational methods to extend the energy conserving model to a general equation of state, and dub the resulting equation set the generalized pseudo-incompressible (GPI) model.We show that the GPI equations suitably capture low-frequency phenomena in both convection and radiative zones in stars and other stratified systems, and we provide recommendations for converting low-Mach number codes to this equation set.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| 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".