Math Colloquium: Fri at 2:30pm-3:20pm, CH 443

Title. Geometry and turbulent dissipation in 3D fluid flows

Abstract. Experiments, as well as computational simulations of turbulent

flows indicate that the regions of intense fluid activity organize

in coherent vortex structures, and in particular, in vortex

filaments.

Identifying the role that the vortex filaments play in the theory of

turbulent cascades and turbulent dissipation in 3D (incompresible,

viscous) flows, modeled by the 3D Navier-Stokes equations, has

been one of the central problems in turbulence since G.I. Taylor's

fundamental work in the 1930's. Mainly based on measurements of

the wind tunnel turbulence past a uniform grid, Taylor concluded

his observations with the following,

"It seems that the stretching of vortex filaments must be

regarded as the principal mechanical cause of the high rate

of dissipation which is associated with turbulent motion".

The goal of this lecture is to present an overview of a recent

work featuring several rigorous, mathematical results--derived

directly from the 3D Navier-Stokes equations--supporting

Taylor's view on turbulent dissipation.

## April 22, Zoran Grujic, University of Virginia

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