The prestigious Simons Foundation of New York has announced funding for an international project to revisit the fundamental problems of fluid turbulence using statistical mechanics.
The international consortium involves researchers from several French laboratories, including Freddy Bouchet of Laboratoire de Physique at ENS de Lyon, Laurette Tuckerman of ESPCI and Yves Pomeau of École Polytechnique.
He also involves Nigel Goldenfeld of the University of Illinois, Dwight Barkley of the University of Warwick, Björn Hof of the Institute of Science and Technology Austria, Gregory Falkovich of the Weizmann Institute of Science, Brad Marston of Brown University, Steve Tobias of Leeds University and Gregory Eyink of Johns Hopkins University.
The richness of turbulence continues to pose a major challenge to theoretical physics. Due to the wide range of length and time scales intrinsic to the problem, the number of degrees of freedom in 3-D makes even detailed simulation of real turbulent flows challenging. This project uses novel statistical mechanics approaches to explore how fluids become turbulent and their properties in the strongly fluctuating turbulent state itself. Turbulence has two potentially universal scaling regimes: transitional (presumably a critical phenomenon) and high Reynolds number (presumably an asymptotic regime controlled by anomalies and associated phenomena). Thus, we approach turbulence by detailed exploration of these two scaling regimes and connect these limiting cases by advancing the understanding of turbulence-mean flow/large-scale flow interactions to form a complete narrative of turbulence from nonequilibrium statistical mechanics.
This project is loosely organized along four main directions: transitional flows, mean-flow turbulent interactions, fully developed turbulence and experimental studies. Due to a commonality of conceptual and mathematical tools, there are close synergies between these directions, with personnel actively and collaboratively engaged in multiple topics.
The transition to turbulence has now been shown in one experimental system and one computational model to be a nonequilibrium transition in the directed percolation universality class. Above this transition, real flows are dominated by the emergence or imposition of mean flows that interact with turbulence with feedback in both directions. Our goal is to construct a nonequilibrium statistical theory, including the description of rare events, that characterizes the interaction of mean flows with turbulence, both in the case where the mean flow emerges self-consistently from correlations in the turbulence and where the turbulence is driven by the mean flow. An important role is played here by extreme, rare events and multi-stability. The challenge on the experimental side is to characterize scaling laws for dissipative processes accurately and on the theoretical side, to understand how they emerge and persist up to large Reynolds numbers.
At asymptotically large Reynolds numbers, turbulence exhibits strongly singular behavior. In fact, our perspective is that it may not even be fruitful to view it as strong fluctuations about a uniform background, but rather that strong space-time localized bursts are the zeroth order solution about which one has to construct a theory. In this regime, stochasticity emerges spontaneously and fluctuations exhibit strong and anomalous behavior that calls out for renormalization group methods and related field theoretic techniques to be employed.
The Simons Foundation
The Simons Foundation is a private foundation established in 1994 by Marilyn and James Harris Simons with offices in New York City. The foundation funds research in mathematics and the basic sciences.