|Indiana Jones vs. Fancy Footwork|
- 31. “Turbulence” - a one spatial dimension warmup
- 32. Turbulence?
- The last of all homeworks
- Course conclusion
Flows described by PDEs are said to be `infinite dimensional' because if one writes them down as a set of ODEs, one needs infinitely many of them to represent the dynamics of one PDE. The long-time dynamics of many such systems of physical interest is finite-dimensional. Here we cure you of the fear of infinite-dimensional flows.
In the world of everyday, moderately turbulent fluids flowing across planes and down pipes, a velvet revolution is taking place. Experiments are as detailed as simulations, there is a zoo of exact numerical solutions that one dared not dream about a decade ago, and portraits of turbulent fluid's state space geometry are unexpectedly elegant. We take you on a tour of this newly breached, hitherto inaccessible territory. Mastery of fluid mechanics is no prerequisite, and perhaps a hindrance: the tutorial is aimed at anyone who had ever wondered how we know a cloud when we see one, if no cloud is ever seen twice? And how do we turn that into mathematics?
Tutorial - A stroll through 61,506 dimensions
Ladies and gentlemen, this is no model: this is Navier-Stokes!
|What have we learned?|
|Gutzwiller semiclassical quantization|
|Be brave: do QFT|
|From fluid dynamics to Yang-Mills|
|Knowing where to stop: h-bar|
|Turbulence (optional: earn bonus points)|
|Discussion forum for week 16|
|Symmetries of the solutions|
|Equilibria of equilibria|
|Daniel Kleppner - Quantum Mechanics and Chaos|
|Richard Feynman - The Principle of Least Action|