Exact coherent structures in transitional flows: Dynamics and localization (INVITED)

Abstract eng:
Invariant solutions of the Navier-Stokes equations provide a mathematically sound framework for the long-standing idea of coherent structures in turbulence. In recent years, computations of weakly unstable equilibria, traveling waves, and periodic orbits have shed much light on the structure and dynamics of transitional of shear flows. In this talk we present (1) a brief overview of the methodology and goals of invariant solutions or exact coherent structures as framework for analyzing transitional turbulence, and (2) recent results that extend invariant solutions from spatially periodic solutions in minimal flow units to localized solutions in extended flows. The localized solutions provide precise specifications of coherent structures long observed in turbulent shear flows and are potentially a first step towards an understanding of the spatiotemporal dynamics of turbulence as a system of self-organized, interacting coherent structures.

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