MATH-GA.3001-001 Geophysical Fluid Dynamics
This course serves as an introduction to the fundamentals of geophysical fluid dynamics. No prior knowledge of fluid dynamics will be assumed, but the course will move quickly into the subtopic of rapidly rotating, stratified flows. Topics to be covered include (but are not limited to): the advective derivative, momentum conservation and continuity, the rotating Navier-Stokes equations and non-dimensional parameters, equations of state and thermodynamics of Newtonian fluids, atmospheric and oceanic basic states, the fundamental balances (thermal wind, geostrophic and hydrostatic), the rotating shallow water model, vorticity and potential vorticity, inertia-gravity waves, geostrophic adjustment, the quasi-geostrophic approximation and other small-Rossby number limits, Rossby waves, baroclinic and barotropic instabilities, Rayleigh and Charney-Stern theorems, geostrophic turbulence. Students will be assigned bi-weekly homework assignments and some computer exercises, and will be expected to complete a final project. This course will be supplemented with out-of-class instruction.
- Vallis, G.K. (2006). Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-scale Circulation. New York, NY: Cambridge University Press.
- Salmon, R. (1998). Lectures on Geophysical Fluid Dynamics. New York, NY: Oxford University Press.
- Pedlosky, J. (1992). Geophysical Fluid Dynamics (2nd ed.). New York, NY: Springer-Verlag.