Seminar Analysis and Mathematical Physics: Roman Shvydkoy (University of Illinois at Chicago)

Volumetric approach to intermittency in fully developed turbulence

The classical Kolmogorov-41 theory of turbulence is based on a set of  pivotal assumptions on scaling and energy dissipation for solutions satisfying incompressible fluid models. In the early 80's experimental evidence emerged that pointed to departure from the K41 predictions, which was attributed to the phenomenon of statistical intermittency.  In this talk we give an overview of the classical results in the subject, relationship of intermittency to the problem of global well-posedness of the 3D Navier-Stokes system, and discuss a new approach developed jointly with A. Cheskidov on how to measure and study intermittency from a rigorous perspective.  At the center of our discussion will be a new interpretation of an intermittent signal described by volumetric properties of the filtered field.  It provides, in particular, a systematic approach to the Frisch-Parisi multifractal formalism, and recasts intermittency from the point of view of information theory. 

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