MATHEMATICAL PHYS
ICS WEBINAR
RUTGERS UNIVERSITY
__________________________________________
Gregory Eyink – Joh ns Hopkins University
Wednesday, March 27th, 10:45AM EDT (Zoom me eting starts at 10:30 EDT)
Fluid Turbulence and Statistical&n bsp;Physics Collide
We present an overview of recent&
nbsp;developments in fluid turbulence and new perspectives that they s
uggest in statistical physics. We begin with studies of effe
cts of thermal fluctuations in very low Reynolds-number turbulence, wh
ich challenge the view of "macroscopic fluctuation theory” that h
ydrodynamic behavior arises as a law of large numbers in a “
scaling limit.” Instead, these studies support an alternative ide
a that fluctuating hydrodynamics originates from molecular dynamics as
a low-wavenumber “effective field theory”. This point of view has imp
lications also for laminar flows. For example, an asymptotic high
-Schmidt theory of liquid diffusion by Donev, Fai and vanden-Eijn
den based on nonlinear fluctuating hydrodynamics predicts that non-equ
ilibrium concentration fluctuations in a liquid at rest subject to a c
oncentration gradient arise by a turbulent cascade process. This
cascade generates non-Gaussian fluctuations with order unity skew
ness and flatness, inconsistent with a central limit theorem. Exp
erimental measurement of these higher-order correlations may therefore be&n
bsp;able to distinguish between “effective field theory” and “macroscopic f
luctuation theory”. Furthermore, we present evidence that even at
very high Reynolds numbers effects of tiny thermal fluctuations
can randomize the largest eddies of a turbulent flow, contradicting a
deterministic “law of large numbers”. This effect arises from “spontaneous&
nbsp;stochasticity”, a weak-noise critical behavior associated to an i
nfinite number of fluid histories with zero Onsager-Machlup
;action (deterministic Euler solutions), analogous to infinitely many groun
d states in mean-field spin glasses. Exact renormalization group analy
sis of simple 1D models of spontaneous stochasticity derives a no
vel “singular large deviations” mediated by non-unique zero-actio
n histories, distinct from the standard large-deviations due to&n
bsp;weak-noise instantons which is predicted by macroscopic fluctuation&nbs
p;theory.
This talk is based on joint work with Nigel G
oldenfeld, Dima Bandak, Alexei Mailybaev, John Bell, Alej Garcia,
Andy Nonaka, and Amir Jafari.