Mantle convection models with temperature‐ and depth‐dependent thermal expansivity
Bibliographic record
Abstract
We investigate the effects of temperature‐ and depth‐dependent thermal expansivity in two‐dimensional mantle convection models in cylindrical shell and plane layer geometries. Most previous models of mantle convection have employed either a constant coefficient of thermal expansion, α, or a depth‐dependent α = α(r), where r is the radial coordinate antiparallel to gravity. We consider α to have the form α(r,T) = αr (r)αT (T), where αr(r) increases with radius, r (or decreases with depth), and αT (T) increases with temperature, T. We find that the depth dependence and temperature dependence of α each have a significant, but opposite, effect on the mean surface heat flux (or Nusselt number) and the mean surface velocity of the convecting system. For α = αr (r), a decrease of α with depth by a factor of 4 across the mantle causes a decrease of surface heat flux by about 20% and a decrease in mean surface velocity by about 30%, relative to the constant α case, in either cylindrical or plane layer geometry. However, when the temperature dependence of α is also included, αT (T) effectively compensates for the effects of αr(r) such that the predicted decreases in heat flow and surface velocity are either eliminated or, in some cases, become increases. Consequently, previous studies that include only the effects of depth dependence of α may underestimate surface heat flow and plate velocities by as much as 20% and 50%, respectively.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".