Mathematical Fluid Dynamics of Atmospheric and Oceanic Flows

Explore the mathematical foundations of atmospheric and oceanic fluid dynamics in this 44-minute lecture by Robin S. Johnson at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the application of general fluid dynamics equations to describe planetary-scale flows using the thin-shell approximation. Discover how rotating spherical coordinates and Earth's geoid are incorporated into the mathematical model. Learn about the philosophy of mathematical fluid dynamics and its emphasis on minimal approximation. Examine the perturbation of stationary background states in atmospheric modeling, including dynamics and thermodynamics. Understand how this comprehensive approach recovers familiar theoretical results while offering novel applications. Conclude with a brief overview of the formulation's application to oceanic flows. Gain insights into the mathematical intricacies of Earth's fluid systems through this advanced exploration of atmospheric and oceanic dynamics.