Colloquium: Predrag Cvitanovic (with M. Gudorf, N.B. Budanur and B. Gutkin) / Center for Nonlinear Science, Georgia Tech

Event Date: 

Thursday, January 26, 2017 - 3:30pm to 4:30pm

Event Location: 

  • 6635 South Hall
Title: Is space time? A spatiotemporal theory of transitional turbulence
Abstract: Recent advances in fluid dynamics reveal that the recurrent flows observed in moderate Reynolds number turbulence result from close passes to unstable invariant solutions of Navier-Stokes equations. By now hundreds of such solutions been computed for a variety of flow geometries, but always confined to small computational domains (minimal cells).
The 2016 Gutkin and Osipov paper on many-particle quantum chaos opens a path to determining such solutions on spatially infinite domains. Flows of interest (pipe, channel flows) often come equipped with D continuous spatial symmetries. If the theory is recast as a (D+1)-dimensional space-time theory, the space-time invariant solutions are (D+1)-tori (and not the 1-dimensional periodic orbits of the traditional periodic orbit theory). The symbolic dynamics is likewise (D+1)-dimensional (rather than a single temporal string of symbols), and the corresponding zeta functions should be sums over tori, rather than 1-dimensional periodic orbits. In this theory there is no time, there is only a repertoire of admissible spatiotemporal patterns.