Effects of spatially varying roof cooling on thermal convection at high Rayleigh number in a fluid with a strongly temperature-dependent viscosity
Bibliographic record
Abstract
We investigate the effects of an insulating lid of variable spatial extent on convection in the stagnant-lid regime under thermally steady-state conditions. Using a combination of laboratory experiments, numerical simulations and scaling analyses we characterize the qualitative structure and quantitative heat transfer properties of flows in terms of the fractional extent L of an insulating lid applied at the cold boundary, the thermal resistance of the lid, the magnitude of the temperature dependence of the fluid viscosity Λ and the effective Rayleigh number Ra e for the composite system. A partial insulating lid has two main effects: (i) To increase the mean interior temperature and reduce the average viscosity of the system, which enhances fluid motions, and (ii) to impart a lateral asymmetry to the thermal structure of the cold boundary that leads, in turn, to lateral temperature gradients that drive an overturning flow. Consequently, whereas flow in the uninsulated stagnant-lid regime is in the form of ‘small-scale’ rising and sinking thermals, there is an additional ‘large-scale’ circulation in the presence of partial insulation. The structure, wavelength and heat transfer properties of this large-scale stirring depends on L , Λ and Ra e . For given Ra e – Λ conditions we find optimal values of L at which there occur well-defined maxima in the rate of overturn, the local heat flux carried into the uninsulated part of the cold boundary and in the global average heat flux Nu carried across the system. Whereas both the rate of overturning and local heat flux are associated with the largest lateral temperature gradients, the optimal basal heat flux depends also on a tradeoff with the fractional surface area of the lid. Remarkably, maximal values of the global heat flux can significantly exceed that of the uninsulated stagnant-lid case. The occurrence of such maxima is insensitive to the mechanical boundary conditions applied and is not strongly influenced by lid shape. However, the magnitude and location of optimal heat fluxes depends in a complicated way on the lid surface area and shape, as well as the structure of the hot and cold boundary layers and the wavelength of the large-scale flow.
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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) | 0.000 | 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".