Non-equilibrium statistical mechanics of the turbulent energy cascade: irreversibility and response functions

Abstract

The statistical properties of turbulent flows are fundamentally different from those of systems at equilibrium due to the presence of an energy flux from the scales of injection to those where energy is dissipated by the viscous forces: a scenario dubbed "direct energy cascade". From a statistical mechanics point of view, the cascade picture prevents the existence of detailed balance, which holds at equilibrium, e.g. in the inviscid and unforced case. Here, we aim at characterizing the non-equilibrium properties of turbulent cascades in a shell model of turbulence by studying an asymmetric time-correlation function and the relaxation behavior of an energy perturbation, measured at scales smaller or larger than the perturbed one. We shall contrast the behavior of these two observables in both non-equilibrium (forced and dissipated) and equilibrium (inviscid and unforced) cases. Finally, we shall show that equilibrium and non-equilibrium physics coexist in the same system, namely at scales larger and smaller, respectively, of the forcing scale.

REVTeX 4.2, 15 pages, 10 figures

References in corpus (10)

• Fluctuation-Dissipation: Response Theory in Statistical Physics
• On the thermal equilibrium state of large scale flows
• Turbulence: does energy cascade exist?
• Statistical Equilibrium of Large Scales in Three-Dimensional Hydrodynamic Turbulence
• The effect of helicity on the correlation time of large scale turbulent flows
• Time irreversibility and multifractality of power along single particle trajectories in turbulence
• Response and flux of information in extended non-equilibrium dynamics
• Correlation function and linear response function of homogeneous isotropic turbulence in the Eulerian and Lagrangian coordinates
• Response function of turbulence computed via fluctuation-response relation of a Langevin system with vanishing noise
• A handy fluctuation-dissipation relation to approach generic noisy systems and chaotic dynamics

Cited by in corpus (2)

• Conceptual and practical approaches for investigating irreversible processes
• Turbulent cascade arrests and the formation of intermediate-scale condensates