Available energy of symmetric circulations with application to the middle atmosphere
Bibliographic record
Abstract
We present a theory of available energy for symmetric circulations of a rotating, stratified fluid. The theory is a generalization of the classical theory of available potential energy (APE), in that it accounts for both the momentum and the thermal constraints on the circulation. The generalization relies on the Hamiltonian structure of the conservative dynamics, although (as with classical APE) it still defines the energetics in a non-conservative framework. The energy budget is derived for the circulation transverse to a given balanced reference flow. For a simple example, it is shown that by including momentum constraints, the available energy of the transverse circulation to a symmetrically stable flow is zero, while the energetics of a mechanically driven symmetric circulation properly reflect its causality. The theory is then applied in the context of the primitive equations in spherical coordinates, to diagnose the available energy of the residual mean meridional circulation of the middle atmosphere. Both simulated fields from the Canadian Middle Atmosphere Model and the ERA-40 re-analysis data are used for diagnostic comparison. With the non-resting reference state constructed using the radiative equilibrium temperature the available energy diagnostic robustly identifies the circulation as being thermally damped and mechanically forced, in both the stratosphere and mesosphere, which agrees with its causality. The boundary flux term and the thermal forcing are both negative, with the mechanical forcing, due to deposition of momentum by the waves breaking in-situ, being identified as the driving agent; this agrees with the gyroscopic pumping mechanism as the driving process of the middle atmosphere meridional circulation. In contrast, with the resting (Lorenz-like) reference state the thermal forcing is seen as driving the circulation in the stratosphere (along with the boundary flux), with mechanical forcing being identified as a damping. In the mesosphere the diagnostic with the resting reference state does not encounter a causality problem, with the thermal forcing being identified as damping, and the mechanical forcing along with the boundary flux being the driving agent. However, the circulation is diagnosed as being less strongly forced compared to the non-resting reference state.
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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 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".