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.