週次 |
日期 |
單元主題 |
第1週 |
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Course introduction: why studying Rossby waves, instabilities, and wave-mean-flow interactions? |
第2週 |
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Review of shallow-water systems (momentum and mass conservation, vorticity equation, PV, and circulation theorem) |
第3週 |
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1. Circulation theorem & PV
2. Review of shallow-water waves (SW gravity, inertio-gravity waves; Kelvin; Rossby wave is left for later) |
第4週 |
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Review of shallow-water waves (SW gravity, inertio-gravity waves; Kelvin; Rossby wave is left for later) |
第5週 |
10/20 |
1. Geostrophic adjustment
2. Shallow-water quasi-geostrophic equations & invertibility |
第6週 |
10/27 |
Shallow-water QG and Rossby wave
1. Dispersion relation, PV gradient
2. Phase and energy propagation |
第7週 |
11/03 |
1. Continuously stratified QG
2. Baroclinic instability I: Eady model |
第8週 |
11/10 |
Project 1:
Rossby wave from an oscillatory source (Haidvogel & Rhines 83)
Stationary Rossby waves |
第9週 |
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Baroclinic instability II: Eady model
1. Growth rate, wave modes, and vertical structure
2. Physical interpretations via Rossby wave interactions |
第10週 |
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Baroclinic instability III
1. Phillips problem and Beta effect
Barotropic instability & Stability criterion (informal look) |
第11週 |
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Introduction to 2D turbulence
1. Inertial range --- Kolmogorov spectrum
2. Energy & enstrophy conservation
3. 3D vs. 2D and QG analogies |
第12週 |
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Project 2: Simulations of Eady and Phillips problems
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第13週 |
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Wave-mean-flow interaction I (in 2D flow)
1. Motivations: observations of surface westerlies
2. Eddy vorticity flux ---- Taylor identity & link to circulation theorem
3. Psudomomentum & non-acceleration theorem
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第14週 |
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Lab experiments or Paper discussion (TBD) |
第15週 |
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Wave-mean-flow interaction II (in continuously stratified QG flow)
1. Eliassen–Palm flux & Rossby wave propagation
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第16週 |
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Wave-mean-flow interaction III
1. Transformed Eulerian mean (TEM): Eulerian vs residual circulation
2. Eddy form stress |
第17週 |
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Project 3 : Zonal jet formation via stochastic forcing
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