Introduction to Geophysical Fluid

• Density and Equation of State for air/water (review/optional)
• Compressibility and potential density/temperature (review/optional)
• Hydrostatic balance in a fluid at rest
• Static stability
• Scaling and Scale Analysis
• Hydrostatic approximation and pressure coordinates
• Boussinesq approximation
• Rotating reference frame
• Equation of motion for stratified, rotating incompressible flow on a sphere
• The f-plane approximation

Shallow Water Equations and Two Layer Approximation

• Rotating linear SWE on an f-plane
• Poincare waves, dispersion and group velocity
• Inertial oscillations
• Geostrophic balance and Margules relation
• Rossby adjustment problem
• Potential vorticity and Kelvin’s circulation theorem
• Kelvin waves

Continuously Stratified Geophysical Fluid

• Linear internal inertia-gravity wave
• Geostrophic adjustment and thermal wind balance
• Circulation, vorticity and potential vorticity

Frictional Effects in Geophysical Fluid

• Eddy viscosity and Ekman layer
• Spin-up and spin-down of geophysical fluid

Effects of Non-uniform Potential Vorticity

• Non-uniform background potential vorticity: the beta effect and the topographic beta effect
• Rossby waves in shallow water: a physical discussion
• A quasi-geostrophic theory of planetary Rossby waves