Instantons and the path to intermittency in turbulent flows

Abstract

Processes leading to anomalous fluctuations in turbulent flows, referred to as intermittency, are still challenging. We consider cascade trajectories through scales as realizations of a stochastic Langevin process for which multiplicative noise is an intrinsic feature of the turbulent state. The trajectories are conditioned on their entropy exchange. Such selected trajectories concentrate around an optimal path, called instanton, which is the minimum of an effective action. The action is derived from the Langevin equation, estimated from measured data. In particular instantons with negative entropy pinpoint the trajectories responsible for the emergence of non-Gaussian statistics at small-scales.

arXiv commentaccepted for publication in PRL, 5 pages, 2 figures

References in corpus (32)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• State-dependent diffusion: thermodynamic consistency and its path integral formulation
• Instantons in Burgers Equation
• Instantons and Intermittency
• Fluctuation Relations for Diffusion Processes
• Rogue Waves and Large Deviations in Deep Sea
• Intermittency of Burgers' Turbulence
• Viscous Instanton for Burgers' Turbulence
• The instanton method and its numerical implementation in fluid mechanics
• A rare event algorithm links transitions in turbulent flows with activated nucleations
• Instanton for random advection
• On the universality of small scale turbulence
• Instanton for the Kraichnan Passive Scalar Problem
• Symmetric path integrals for stochastic equations with multiplicative noise
• An Iterative Procedure for the Estimation of Drift and Diffusion Coefficients of Langevin Processes
• The Fokker-Planck Approach to Complex Spatio-Temporal Disordered Systems
• Experimental Evidence of Hydrodynamic Instantons: The Universal Route to Rogue Waves
• Estimation of drift and diffusion functions from time series data: A maximum likelihood framework
• Improved estimation of Fokker-Planck equations through optimisation
• Probing small-scale intermittency with a fluctuation theorem
• Computation of rare transitions in the barotropic quasi-geostrophic equations
• On universal features of the turbulent cascade in terms of non-equilibrium thermodynamics
• A Langevin equation for the energy cascade in fully-developed turbulence
• Vorticity statistics in the direct cascade of two-dimensional turbulence
• Multistability and rare spontaneous transitions in barotropic $\beta$-plane turbulence
• Instanton Calculus in Shell Models of Turbulence
• Instantons in a Lagrangian model of turbulence
• Velocity-Gradient Probability Distribution Functions in a Lagrangian Model of Turbulence
• About coherent structures in random shell models for passive scalar advection
• Instantons and Fluctuations in a Lagrangian Model of Turbulence

Cited by in corpus (6)

• An open source MATLAB package to perform basic and advanced statistical analysis of turbulence data and other complex systems
• Infinite ergodicity for geometric Brownian motion
• Evaluation of transition rates from nonequilibrium instantons
• Scalable Methods for Computing Sharp Extreme Event Probabilities in Infinite-Dimensional Stochastic Systems
• Short-time expansion of one-dimensional Fokker-Planck equations with heterogeneous diffusion
• The effective diffusion constant of stochastic processes with spatially periodic noise