Geophysical Fluid Dynamics - Reading (MTH 35X.5)

Course Syllabus: 

• Equations of motion and approximations- Momentum equations for fluid on a rotating frame, continuity equations, thermodynamic equations, scalings, Boussinesq Approximation, Anelastic Approximation
• Shallow Water systems theory- Single layer and stratified Shallow Water systems, Shallow Water waves
• Vorticity and Circulation- Vorticity and Circulation Theorems, Potential Vorticity in Approximate-Stratified Models
• Geostrophic theory- The Planetary-Geostrophic Equations, Quasi-Geostrophic Equations, Ekman layer
• Waves in the atmosphere-ocean system- Rossby waves, Gravity waves, Internal waves, Equatorial wave disturbances, Waves-mean flow interactions
• Instabilities in geophysical fluids- Instability of Parallel Shear Flow, Barotropic and baroclinic instabilities, Energetics
• Turbulence- The Kolmogorov Theory, 2D and 3D turbulence, geostrophic turbulence, turbulent diffusion and mixing

Course Outcome: After this course the student will

• gain a fundamental understanding of the fluid dynamics of the atmosphere and the oceans.
• appreciate turbulent flow structures at large scales of the planet
• examine different kinds of dispersive waves and their energetics across scales