3T350 - Chaos

This course is the continuation of 3T220 (Chaos), but now with a greater emphasis on the application of Chaos concepts to fluids. Chaos is the seemingly erratic behavior of simple deterministic, but nonlinear dynamical systems. We will first discuss the route to chaos, where we will already encounter the scaling concepts that will return in the description of chaotic fluid flow and turbulence. After a discussion of basic concepts, such as the sensitivity to variation in initial conditions, and the multifractal organization of phase space, we will introduce chaotic behavior and synchronization in coupled systems. These scaling ideas will then be carried over to the description of turbulence, the erratic flow of a fluid. We will do this in both the Eulerian and Lagrangian frame, where we move with the flow. While turbulence is wild chaos, also stirred viscous fluids may be chaotic, which may help to efficiently stir tracers. Also this case will be analyzed with the tools introduced in this course, such as local sensitivity to perturbations, and scaling of the concentration field of the stirred material. Central to the course is the exposure to the modern literature, in particular papers which appeared in Physical Review Letters (the most famous Physics journal). These papers can serve as inspiration for student presentations. Of course, adequate coaching is offered here.

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