Heat Transport in Low-Rossby-Number Rayleigh-Bénard Convection
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Full frame distilled prediction
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.
- Candidate categories
- none
- Consensus categories
- none
- Domain
- Candidate signal: noneConsensus signal: none
- Study design
- Candidate signal: Simulation or modelingConsensus signal: Simulation or modeling
- Genre
- Candidate signal: EmpiricalConsensus signal: Empirical
- Teacher disagreement score
- 0.293
- Threshold uncertainty score
- 0.651
- Validation status
machine_predicted_unvalidated·codex-gemma-dda1882f352a
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)
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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.
- Teacher spread
- 0.226 · how far apart the two teachers sit on this one work
- Validation status
score_only:v0-immature-baseline· verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it
Abstract
We demonstrate, via simulations of asymptotically reduced equations describing rotationally constrained Rayleigh-B\'enard convection, that the efficiency of turbulent motion in the fluid bulk limits overall heat transport and determines the scaling of the nondimensional Nusselt number $\mathrm{Nu}$ with the Rayleigh number $\mathrm{Ra}$, the Ekman number $E$, and the Prandtl number $\ensuremath{\sigma}$. For $E\ensuremath{\ll}1$ inviscid scaling theory predicts and simulations confirm the large $\mathrm{Ra}$ scaling law $\mathrm{Nu}\ensuremath{-}1\ensuremath{\approx}{C}_{1}{\ensuremath{\sigma}}^{\ensuremath{-}1/2}\mathrm{R}{\mathrm{a}}^{3/2}{E}^{2}$, where ${C}_{1}$ is a constant, estimated as ${C}_{1}\ensuremath{\approx}0.04\ifmmode\pm\else\textpm\fi{}0.0025$. In contrast, the corresponding result for nonrotating convection, $\mathrm{Nu}\ensuremath{-}1\ensuremath{\approx}{C}_{2}\mathrm{R}{\mathrm{a}}^{\ensuremath{\alpha}}$, is determined by the efficiency of the thermal boundary layers (laminar: $0.28\ensuremath{\lesssim}\ensuremath{\alpha}\ensuremath{\lesssim}0.31$, turbulent: $\ensuremath{\alpha}\ensuremath{\sim}0.38$). The $3/2$ scaling law breaks down at Rayleigh numbers at which the thermal boundary layer loses rotational constraint, i.e., when the local Rossby number $\ensuremath{\approx}1$. The breakdown takes place while the bulk Rossby number is still small and results in a gradual transition to the nonrotating scaling law. For low Ekman numbers the location of this transition is independent of the mechanical boundary conditions.
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The record
- Venue
- Physical Review Letters
- Topic
- Fluid Dynamics and Turbulent Flows
- Field
- Engineering
- Canadian institutions
- Canadian Institute for Theoretical AstrophysicsUniversity of Toronto
- Funders
- National Science Foundation
- Keywords
- PhysicsPrandtl numberRossby numberNusselt numberRayleigh numberEkman numberTurbulenceScalingLaminar flowConvectionBoundary layerThermodynamicsMechanicsClassical mechanicsNatural convectionReynolds numberGeometryMathematics
- Has abstract in OpenAlex
- yes