TITLE: Is turbulence a critical phenomenon?
SPEAKER: Nigel Goldenfeld
ABSTRACT: Are fluid turbulence and critical phenomena analogous to one another? In this talk, I try to emulate the pattern of discovery which led to the solution of the phase transition problem, and show how critical scaling ideas lead to the prediction of a novel scaling law --- a manifestation of what I term roughness-induced criticality.
This scaling law is verified by analyzing experimental data on turbulent pipe flows, taken by Nikuradze in 1933.
The scaling law arises naturally from a connection between the small-scale velocity fluctuations in turbulence and the large-scale macroscopic flow properties such as friction.
This connection is a type of non-equilibrium fluctuation-dissipation theorem, and has been tested by direct numerical simulations and experiments on two-dimensional turbulent flows in soap films.
These ideas refine the notion of what it would mean to have a "complete solution to the problem of turbulence".