Recurrent solutions and dynamics of turbulent flows, as seen in experiments
In the world of moderate, everyday turbulence of fluids flowing across planes and down pipes, a quiet revolution is taking place. Applied mathematicians can today compute 'exact coherent structures', i.e. numerically precise 3D, fully nonlinear Navier-Stokes solutions: unstable equilibria, traveling waves, and (relative) periodic orbits. Experiments carried out at Georgia Tech today yield measurements as detailed as the numerical simulations; our experimentalists measure 'exact coherent structures' and trace out their unstable manifolds. What emerges is a dynamical systems theory of low-Reynolds turbulence as a walk among sets of weakly unstable invariant solutions.
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 talk is aimed at anyone who had ever wondered why - if no cloud is ever seen twice - we know a cloud when we see one? And how do we turn that into mathematics?
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slides: https://ChaosBook.org/overheads/PDEs/...
For theorist's vision, guided tour through
https://ChaosBook.org/tutorials
For those who still can read:
https://ChaosBook/chapters/ChaosBook.pdf#chapter.30
Online course
https://ChaosBook.org/course1
For the experimentalist's vision, beg the heroes of this video to put their talks and movies online, so I am not the only one to know what the big deal here is :)
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GTmath22.mp4