Dynamics of the Earth's fluid core: implementation of a Clairaut coordinate system
Bibliographic record
Abstract
Abstract If the reference state of a rotating and self gravitating fluid body is one of hydrostatic equilibrium then the figure of the body is a spheroid such that a cross sectional area parallel to the equatorial plane of the body is a circle while that parallel to a meridional plane is an ellipse. The effects of the fluid body’s flattened (spheroidal) figure is small on the frequencies of the body’s short-period (shorter than a few hours in the case of the Earth) normal modes. For the long-period normal modes, however, these effects must be considered. Furthermore, the body’s wobble and nutation modes owe their existence to its ellipsoidal figure. In the conventional approach to computing these frequencies, an orthogonal coordinate system is usually considered. It is then necessary to have the knowledge of the derivatives of the material properties of the body, such as the density and Lame parameters, in order to include the effects of the ellipticity in the dynamical equations. In the available Earth models, however, these derivatives are not well defined. In order to minimize the effects of these derivatives in the treatment of the dynamical problems we use a non-orthogonal (Clairaut) coordinate system. Using this approach, we compute the frequencies and displacement eigenfunctions for some of the inertial modes of a realistic spheroidal model of the Earth’s fluid core and compare them to the known results for an Earth model with a homogeneous and incompressible fluid core.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 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".