Linear theory of shallow convection in deep, vertically sheared atmospheres
Bibliographic record
Abstract
The linear theory of vertically sheared convection is extended to deep‐atmosphere flows with arbitrary wind, stability, and diffusion profiles. Consistent with previous findings, reference single‐layer vertical channel flows show fastest growth for shear‐parallel roll circulations and much weaker growth for shear‐transverse circulations, causing the former to dominate. In a more realistic three‐layer setting, where the cloud layer lies between a mixed layer below and a stable free troposphere aloft, shear‐parallel rolls also dominate. However, shear‐transverse rolls grow much faster than before, which degrades the convective organization. An analysis focused on the vertical perturbation phase tilt leads to a novel interpretation of these results. Vertical shear imparts a downshear tilt, which acts to weaken the convective growth driven by dynamic and non‐hydrostatic buoyant vertical perturbation pressure gradients (VPPGs). Whether these VPPGs can maintain growth in the face of the shear depends largely on the Richardson number (Ri), with becoming a necessary condition for (inviscid) growth of shear‐perpendicular rolls in the short‐wave limit. In deeper, three‐layer atmospheres, longer vertical wavelengths are admitted, which fosters less tilted and faster growing perturbations. This effect, however, is partially offset by differential tilting between kinematic and thermal anomalies. Numerical simulations are used to verify the linear results and to explore the evolution of the convection into the nonlinear regime. As the nonlinearities grow, an initial preference for smaller‐scale, shear‐parallel circulations is ultimately overwhelmed by larger‐scale perturbations with no preferred orientation. Thus, the linear findings are most applicable to the early evolution of cloud layers undergoing turbulent transition.
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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 | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 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) | 0.003 | 0.001 |
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".