Syllabus

Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Description

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.