Large eddy simulations of thermal convection at high Rayleigh number
Bibliographic record
Abstract
With the vastly improved speed and the new shared-memory architecture of the current massively parallel systems, it is now possible to simulate thermal convection at very high Rayleigh (Ra) number lying in the turbulent regime. However, both the dynamics and the interaction with the turbulence may be simultaneously important. Even when only the large scales are of interest, we cannot simply ignore the smallest scales because of the feedback from strong non-linearities everywhere in the flow. Large eddy simulation (LES), a time-honoured method in engineering fluid mechanics and meteorology, may be the only way to simulate the time-dependent physics in its full complexity, while keeping a reasonable accuracy at the largest scales in highly non-linear geophysical fluid dynamical flows, such as mantle convection in the early Earth, convection inside the Jovian moons and the geodynamo. We have tested here a LES model based on the Smagorinsky assumption for 2-D turbulent convection for a finite Prandtl (Pr) number fluid with Pr = 1, free-slip boundary conditions and an aspect ratio of 3. The subgrid-scale model is only employed for the temperature equation, where the steepest gradients are developed. The same model can also be used for infinite Prandtl number convection. This LES model has been validated by comparison with direct numerical simulation (DNS) for Ra between 108 and 1010 with a grid up to 512 × 1536 points. Statistical properties of the flow based on LES are presented for the probability distribution functions (PDF) in space and also the spectra describing the thermal and kinetic energy distributions for Ra up to 1010.
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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) | 0.011 | 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".