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Explore the dynamics of ocean waves and wind-driven flows in this comprehensive lecture, the first installment of a mini-course by Nathan Paldor. Delve into the fascinating world of Kelvin-Stuart vortices, classical mixing layer flows with wide-ranging applications in fluid mechanics, plasma physics, and planetary rings. Examine the nonlinear stability of these vortices for co-periodic perturbations and their linear instability for multi-periodic or modulational perturbations. Investigate the appearance of Kelvin-Stuart cat's eyes as magnetic islands in magnetostatic equilibria for 2D ideal MHD equations in plasmas. Learn about the nonlinear stability of these magnetic islands for co-periodic perturbations and gain insights into the rigorous proof of the coalescence instability. This 1-hour and 22-minute lecture, part of the Thematic Programme on "The Dynamics of Planetary-scale Fluid Flows" held at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI), offers a deep dive into the complex interactions between waves, wind, and oceanic flows.
