1. Fluids: air, water. Constitutive equations. Structure of the atmosphere and the ocean. Similarities and differences.
2. Equations of motion in rotating coordinate frame (momentum, mass conservation, energy).
3. Atmosphere as a thin layer of fluid on a rotating sphere. Hydrostatic approximation. Potential temperature, potential density.
4. Multiscale atmospheric and oceanic flows. Filtration of equations. Geostrophic approximation.
5. Prognostic equations. Natural coordinates. Balanced flows in the atmosphere and in the ocean.
6. Shallow water equations. Incopmpressibility: Boussinesq and anelastic approximations.
7. Importance of the atmospheric boundary layer. Oceanic surface layer. Ekman layer in the atmosphere and in the ocean. Ocean -atmosphere interactions.
8. Circulation and vorticity. Potential vorticity. Cyclonic and anticyclonic circulation.
9. Quasi-geostrophic approximation. Numerical Weather Prediction. Mid-latitude circulations.
10. Waves in the atmosphere and in the ocean: acoustic, gravity, inertio-gravity, Rossby waves.
11. Hydrodynamic instabilities in the atmosphere and in the ocean. Baroclinic instability. Mesoscale circulations.
12. Global circulation. Energetics of global circulation. Heat transport in the ocean and in the atmosphere.
Geoffrey K. Vallis, Atmospheric and Oceanic Fluid Dynamics
Benoit Cushman-Roisin, Introduction To Geophysical Fluid Dynamics. Physical and Numerical Aspects
J.R. Holton, An Introduction to dynamic meteorology
M. L. Salby, Fundamentals of Atmospheric Sciences