New York University 3 credits Mathematics
This course serves as an introduction to the fundamentals of geophysical fluid dynamics. No prior knowledge of fluid dynamics is assumed, but the course moves quickly into the subtopic of rapidly rotating, stratified flows. Topics 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, and geostrophic turbulence. Students are assigned biweekly homework assignments and some computer exercises, and are expected to complete a final project or exam.
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