週次 |
日期 |
單元主題 |

第1週 |
9/17 |
course introduction & assignment |

第2週 |
9/24 |
Review of QG system (I): QGPV conservation & invertibility (Vallis 5.3, 5.4)
Study questions:
1. Derive QGPV conservation for single layer and continuous stratified fluid. What are their physical meanings? What are the key assumptions in QG?
2. What are momentum, mass, and buoyancy conservation laws for QG? |

第3週 |
10/01 |
Review of QG system (II): Rossby waves (Vallis 6.4, 6.6)
Study questions:
1. Rossby wave phase and energy propagation (dispersion circle)
2. Existence of RW requires background PV gradients. What sets the background PV gradient? |

第4週 |
10/08 |
Review of QG system (III): Baroclinic instability (Vallis 9.4, 9.5)
Study questions:
1. What are the physical mechanisms for the instability? The necessary condition for instability is that PV gradient must change sign in the domain. What does it mean?
2. Eady growth rate, most unstable mode, westward phase tilt. What are they and what are their significance? |

第5週 |
10/15 |
Review of QG system (IV): Two-layer QG and Phillips model of baroclinic instability (beta effect) (Vallis 9.6, 9.7)
Study questions:
1. Derive and understand the two-layer system. Can you do this from scratch?
2. There is a critical shear and longwave cutoff in the stability curve. Why? |

第6週 |
10/22 |
Exercise I: coding up a two-layer problem
Study questions:
1. Can you implement two-layer QG system using Dedalus?
2. How do you know that your implementation is correct? |

第7週 |
10/29 |
Exercise II: Testing the Phillips problem
Study questions:
1. Can you verify the critical shear in your numerical model?
2. Do the beta effects stabilize or de-stabilize the flow? Why?
3. How do you obtain an equilibrium state? |

第8週 |
11/05 |
Physical interpretation of baroclinic instability
1. mutual reinforcement of boundary-trapped, counter-propagating waves
2. Energectics of QG system |

第9週 |
11/12 |
Review of QG system (V): 2D turbulence phenomenology & inverse energy cascade (Vallis 11.1~11.3)
Study questions:
1. What are the differences between 3D & 2D turbulence?
2. Derive & understand the inertial range argument & KE spectral slopes
3. Why is there an inverse energy cascade & forward enstrophy cascade? |

第10週 |
11/19 |
Review of QG system (IV): Two-layer QG and Phillips model of baroclinic instability (beta effect) (Vallis 9.6, 9.7)
Study questions:
1. Derive and understand the two-layer system. Can you do this from scratch?
2. There is a critical shear and longwave cutoff in the stability curve. Why?
Study questions:
1. What are the predictions of equilibrated eddy length & velocity scales?
2. What are the underlying assumptions in HL96 theory? |

第11週 |
11/26 |
Review of QG system (IV): Two-layer QG and Phillips model of baroclinic instability (beta effect) (Vallis 9.6, 9.7)
Study questions:
1. Derive and understand the two-layer system. Can you do this from scratch?
2. There is a critical shear and longwave cutoff in the stability curve. Why? |

第12週 |
12/03 |
Review of QG system (V): 2D turbulence phenomenology & inverse energy cascade (Vallis 11.1~11.3)
Study questions:
1. What are the differences between 3D & 2D turbulence?
2. Derive & understand the inertial range argument & KE spectral slopes
3. Why is there an inverse energy cascade & forward enstrophy cascade? |

第13週 |
12/10 |
Literature survey (I): Held and Larichev (1996) (HL96) --- Theory of equilibrated eddy scales
Study questions:
1. What are the predictions of equilibrated eddy length & velocity scales?
2. What are the underlying assumptions in HL96 theory? |

第14週 |
12/17 |
Literature survey (II): Scheneider and Walker (2006) --- Atmospheric eddies
Study questions:
1. Are there evidences for inverse energy cascade in atmosphere?
2. If not, why? Is the QG theory of geostrophic turbulence wrong? |

第15週 |
12/24 |
Literature survey (III):
Stammer (1998)--- Oceanic eddy scales (observations)
Smith (2007) --- Oceanic eddies stability calculations |

第16週 |
12/31 |
Discussion about the final project on equilibrated eddy scales |

第17週 |
1/07 |
Project presentation |