MATHEMATICAL PHYSICS WEBINAR
RUTGERS UNIVERSITY
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Gregory Eyink – Johns Hopkins University
Wednesday, March 27th, 10:45AM EDT
Fluid Turbulence and Statistical Physics Collide
We present an overview of recent developments in fluid turbulence and new perspectives that they suggest in statistical physics. We begin with studies
of effects of thermal fluctuations in very low Reynolds-number turbulence, which challenge the view of "macroscopic fluctuation theory” that hydrodynamic behavior arises as a law of large numbers in a “scaling limit.” Instead, these studies support an alternative idea that fluctuating hydrodynamics originates from molecular dynamics as a low-wavenumber “effective field theory”. This point of view has implications also for laminar flows. For example, an asymptotic high-Schmidt theory of liquid diffusion by Donev, Fai and vanden-Eijnden based on nonlinear fluctuating hydrodynamics predicts that non-equilibrium concentration fluctuations in a liquid at rest subject to a concentration gradient arise by a turbulent cascade process. This cascade generates non-Gaussian fluctuations with order unity skewness and flatness, inconsistent with a central limit theorem. Experimental measurement of these higher-order correlations may therefore be able to distinguish between “effective field theory” and “macroscopic fluctuation 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 stochasticity”, a weak-noise critical behavior associated to an infinite number of fluid histories with zero Onsager-Machlup action (deterministic Euler solutions), analogous to infinitely many ground states in mean-field spin glasses. Exact renormalization group analysis of simple 1D models of spontaneous stochasticity derives a novel “singular large deviations” mediated by non-unique zero-action histories, distinct from the standard large-deviations due to weak-noise instantons which is predicted by macroscopic fluctuation theory.
This talk is based on joint work with Nigel Goldenfeld, Dima Bandak, Alexei Mailybaev, John Bell, Alej Garcia, Andy Nonaka, and Amir Jafari.