Representation of Atmospheric Gravity Wave Breaking and Saturation under the Anelastic Approximation
Bibliographic record
Abstract
In this thesis, we present a mathematical model that represents internal gravity waves in the atmosphere using nonlinear partial differential equations and then use analytical and numerical methods. We consider a two dimensional, monochromatic, nonlinear, non-hydrostatic and viscous flow configuration with two types of approximations; Boussinesq and anelastic. In the real atmosphere, gravity wave amplitudes increase with altitude and this can lead to wave breaking. Most previous studies were based on the Boussinesq approximation in which the linear wave solutions do not increase with altitude. We consider a more realistic representation based on the anelastic approximation in which the wave amplitude increases with altitude. We carry out a weakly-nonlinear analysis to derive equations describing then time evolution of the wave-induced mean flow and potential temperature due to the nonlinear interactions. We carry out weakly and fully nonlinear numerical simulations of Boussinesq and anelastic equations. We also carry out numerical simulations to study the anelastic gravity wave propagation, growth, breaking, overturning and its impacts on the mean flow in the atmosphere. Results demonstrate that upward-propagating waves grow to sufficiently large amplitude and eventually break. Results demonstrate that the inclusion of viscosity and heat conduction allows us to investigate the long-term evolution of the gravity wave after wave breaking. It is found that the breaking of the wave field may occur due to two main mechanisms, namely, convective instability and dynamical instability. Convective and dynamical instabilities are examined by the local Richardson number such that convective instability corresponds to situations where the Ri ≤ 0 and dynamical instability corresponds to 0 < Ri < 0.25. The local Richardson number may drop below the stability criterion due to the negative potential temperature gradient, large shear of the velocity perturbation or a combination of both. In general, dynamical instability is more likely to occur at an earlier stage than convective instability. Convective instability is more likely to occur when there is very strong stratification.
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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 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| 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".