課程資訊
課程名稱
地球物理流體力學專題三
Topics in Geophysical Fluid Dynamics (Ⅲ) 
開課學期
109-1 
授課對象
理學院  海洋物理組  
授課教師
陳世楠 
課號
Ocean5127 
課程識別碼
241 U6240 
班次
 
學分
2.0 
全/半年
半年 
必/選修
選修 
上課時間
星期四3,4(10:20~12:10) 
上課地點
海研232 
備註
總人數上限:10人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1091Ocean5127_GFDT 
課程簡介影片
 
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課程概述

The theme of the discussion course for this semester is equilibration of geostrophic eddies in ocean and atmosphere.

Extratropical open ocean and atmosphere are full of eddies that are approximately in geostrophic balance. These eddies are important not only because they are the dominant contributor to the global kinetic energy budget but also they transport momentum and heat that help shapes the mean circulation. For example, estimates using satellite altimetry suggested that the kinetic energy of oceanic mesoscale eddies is around 15 times greater than that of the mean flow. Meridional heat transport of the extratropical troposphere is in large part controlled by transient eddies.

In this course, we will survey some key developments concerning the following questions:

How are the eddies generated and What processes control their velocity and length scales in an equilibrium state?

We will begin by reviewing/studying models of baroclinic instability (assuming that instabilities are important for eddy generation). We will then explore, by following development in literature, if the equilibrated eddy scales can be understood via geostrophic turbulence phenomenology. That is, the size of energy-containing eddies grows until the inverse energy cascade is halted by beta and friction effects.

The course format combines lectures (1/3), student-led presentation (1/3), and numerical experiments (1/3).

Python codes that solve the barotropic vorticity equation will be provided and used. Samples of numerical experiments can be found here:

http://cod-lab.blog.ntu.edu.tw/teaching/ 

課程目標
The objectives are to provide participants opportunities to develop a better understanding for classic GFD problems through discussions and exercises. We learn by helping each others. 
課程要求
Oral presentation and discussion participation 
預期每週課後學習時數
 
Office Hours
 
參考書目
Atmospheric and Oceanic Fluid Dynamics by Vallis (2nd Ed.) and literature 
指定閱讀
待補 
評量方式
(僅供參考)
   
課程進度
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