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Geophysical Fluid Dynamics (GFD)

Illig S. and N. Hall, 2025: Geophysical Fluid Dynamics. Course Material for Master 2 Sciences de l’Océan, de l’Atmosphère et du Climat (SOAC), Toulouse (France) & Cotonou (Benin).


In this course, the goal is not to analyze each phenomenon or process that occurs in the Ocean or the Atmosphere. On contrary, this course aims at integrating all of them into a framework for understanding the dynamics of geophysical fluids in a rotating stratified environment.
  • The PDF of the course is here
  • Videos of the lectures in French and English are available on Nick Hall’s YouTube channel

INTRODUCTION: Overview of Atmosphere and Ocean Dynamics
Before starting the course, we go on a little tour in the Atmosphere and then the Ocean. This will give us a quick overview of the general circulation patterns we can observe in each system. We will highlight some similarities and differences between the Atmosphere and Ocean circulation that will provide insight on the associated dynamics. We use the Earth school web tool

  • Atmosphere dynamics
  • Ocean circulation
  • Course outline and GFD key words

1. Shallow water and vorticity

  • Basic Equations, Balance, and Flow Partition
  • Density Coordinates and Shallow Water Equations
  • Circulation, Vorticity, and Potential Vorticity
  • TD1 questions and solutions

2. Quasi-Geostrophic theory

  • Steady departures from Geostrophy
  • Quasi-Geostrophic Theory I – the f-plane
  • Quasi-Geostrophic Theory II – Expansion in small Rossby number
  • Quasi-Geostrophic Theory III – Applications and Diagnostics

3. Rossby waves and instability

  • Barotropic Rossby waves
  • Baroclinic Rossby waves
  • Barotropic instability
  • Baroclinic instability
  • TD2 questions and solutions
  • TD3 questions and solutions

4. Gravity waves and tropical dynamics

  • Gravity waves in a rotating fluid
  • Boundary Kelvin Waves
  • Equatorial Scaling and Kelvin Wave Solution
  • Equatorial Waves – General Solutions
  • Equatorial Waves – Special Cases and Examples
  • TD4 questions and solutions
  • TD5 questions and solutions

5. Scale interactions in the atmosphere and ocean

  • Scale interactions and Transient Forcing
  • Effect of Transients on the Mean Flow: Closure & Diffusion
  • Systematic Effects of Transient Eddies on Ocean Gyres
  • Examples of Scale Interactions in the Atmosphere
  • Zonal Jets and Turbulence

EPILOGUE: Dynamics on other planets…