Wave Motion in the Ocean and the Atmosphere

Syllabus

Course Meeting Times

Lectures: 3 sessions / week, 1.5 hours / session

Course 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.

Prerequisites

12.800 Fluid Dynamics of the Atmosphere and Ocean

Grading

ACTIVITIES	PERCENTAGES
Homework	60%
Final exam	40%

Basic Topics to be Covered

1. General wave concepts and kinematics
   1. Wave kinematics: amplitude, phase, wave number, frequency, phase velocity, dispersion relation
   2. Method of stationary phase, group velocity, energy flux
   3. Slowly varying media: conservation of crests, ray equations
2. Surface gravity waves
   1. Potential theory, deep-water waves
   2. Shallow water waves
   3. Energy and energy equation
   4. Initial value problem — slowly varying medium
3. Internal gravity waves
   1. Internal wave equation
   2. Unbounded stratified fluid
   3. Internal waves modified by rotation — unbounded fluid
   4. Variable buoyancy frequency — slowly varying medium
   5. The oceanic wave-guide for a stratified, rotating fluid
   6. Internal wave reflection from a solid boundary
4. Waves in homogenous, rotating flows
   1. Laplace’s tidal equations: horizontal and vertical structure equations
   2. Poincare’ and Kelvin waves
   3. Rossby or planetary waves
   4. Quasi-geostrophic Rossby waves
   5. Reflection of Rossby waves
   6. Equatorial beta plane, equatorial waves
5. Topographic effects
   1. Topographic Rossby waves
   2. Bottom-trapped waves
   3. Edge and continental shelf waves
   4. Coastal-trapped waves in a stratified fluid
6. Wave-mean flow interactions
   1. Vertical propagation of waves: steady flow, radiation condition
   2. Rossby waves with stratification
   3. Quasi-geostrophic potential vorticity equation in a stratified atmosphere
   4. Topographically forced, steady Rossby waves over a zonal flow: atmosphere
   5. Waves over a mean flow: ocean
   6. Eady problem
   7. Energetics for instability conditions

Text Books

Pedlosky, Joseph. Waves in the Ocean and Atmosphere Introduction to Wave Dynamics. New York, NY: Springer-Verlag, 2003, p. 260. ISBN: 9783540003403.

Gill, Adrian. Atmosphere-Ocean Dynamics. New York, NY: Academic Press, 1982, p. 662. ISBN: 9780122835223.