本課程介紹旋轉流、層流與旋轉層流中，地球物理波動的基本概念。學科主題始於相速度與群速度這兩個波的共通概念，並涵蓋重力波的力學與動力學，著重於離散、能量通量、初值問題等。用於研究均質層流中內波、慣性波、克耳文波（Kelvin waves）、彭卡瑞波（Poincare waves）與羅士比波（Rossby waves）的學科基礎，亦為課程之重點；拉普拉多潮汐方程式則被運用於赤道波。其他主題還包括：共振交互作用、位渦旋度、波平均流交互作用及不穩定性。

主題

• 序論－動力學：頻率、波數、相位、相速度
  
  
• 內重力波
  • 離散與初值問題
  • 群速度－波包與異質性
  • 能量、波動場、顆粒運動
  • WKB理論
  • 正常模式
  • 垂直擴展－恆定流與輻射條件
    
    
• 表面重力波
  • 運動方程式
  • 初值問題
  • 淺水區域
    
    
• 小尺度旋轉與位渦旋度
  • 慣性內重力波：彭卡瑞波
  • 克耳文波
    
    
• 大尺度流體靜力運動
  • 地轉運動
  • 修正－地轉與重力波
  • 羅士比波
    
    
• 拉普拉斯潮汐方程式與垂直結構方程式
  • 傳統近似法
  • 分離形式－水平與垂直結構方程式
  • 各種波動
    
    
• 赤道ß-平面與赤道波
  
  
• 層狀準地轉運動與不穩定性
  • 地形波與邊界波
  • 不穩度
  • 波平均流交互作用

參考資料:

對於本課程，Joe Pedlosky自有一套相當棒的講稿，相信日後定會出版成冊。

This course is an introduction to basic ideas of geophysical wave motion in rotating, stratified, and rotating-stratified fluids. Subject begins with general wave concepts of phase and group velocity. It also covers the dynamics and kinematics of gravity waves with a focus on dispersion, energy flux, initial value problems, etc. Also addressed are subject foundation used to study internal and inertial waves, Kelvin, Poincare, and Rossby waves in homogeneous and stratified fluids. Laplace tidal equations are applied to equatorial waves. Other topics include: resonant interactions, potential vorticity, wave-mean flow interactions, and instability.

Topics

• Introduction - Kinematics: Frequency, Wavenumber, Phase, Phase Speed
  
  
• Internal Gravity Waves
  • Dispersion and the initial value problem
  • Group velocity - wave packets and inhomogeneities
  • Energy, fields of motion, particle movements
  • WKB theory
  • Normal modes
  • Vertical propagation - steady flow and the radiation condition
    
    
• Surface Gravity Waves
  • Equations of motion
  • Initial value problem
  • Shallow water
    
    
• Rotation and Potential Vorticity - Small Scale
  • Inertial-internal gravity waves, Poincare' waves
  • Kelvin waves
    
    
• Large-Scale Hydrostatic Motions
  • Geostrophic motion
  • Adjustment - Geostrophic and gravity waves
  • Rossby waves
    
    
• Laplace Tidal Equations and The Vertical Structure Equation
  • Traditional approximation
  • Separable form - Horizontal and vertical structure equations
  • All kinds of waves
    
    
• Equatorial ß-Plane and Equatorial Waves
  
  
• Stratified Quasi-Geostrophic Motion and Instabilities
  • Topographic waves and boundary waves
  • Instabilities
  • Wave-mean interactions

Reference:

Joe Pedlosky has an excellent set of notes from his version of this course, which, I believe, will be published as a book.