Constrained Reversible system for Navier-Stokes Turbulence: evidence for Gallavotti's equivalence conjecture

Abstract

Following the Gallavotti's conjecture, Stationary states of Navier-Stokes fluids are proposed to be described equivalently by alternative equations besides the NS equation itself. We propose a model system symmetric under time-reversal based on the Navier-Stokes equations constrained to keep the Enstrophy constant. It is demonstrated through high-resolved numerical experiments that the reversible model evolves to a stationary state which reproduces quite accurately all statistical observables relevant for the physics of turbulence extracted by direct numerical simulations at different Reynolds numbers. The possibility of using reversible models to mimic turbulence dynamics is of practical importance for coarse-grained version of Navier-Stokes equations, as used in Large-eddy simulations. Furthermore, the reversible model appears mathematically simpler, since enstrophy is bounded to be constant for every Reynolds. Finally, the theoretically interest in the context of statistical mechanics is briefly discussed.

References in corpus (5)

• Fluctuation-Dissipation: Response Theory in Statistical Physics
• Equivalence of Non-Equilibrium Ensembles and Representation of Friction in Turbulent Flows: The Lorenz 96 Model
• Self-similar Subgrid-scale Models for Inertial Range Turbulence and Accurate Measurements of Intermittency
• On the local energy flux of turbulent flows
• On the probability distribution of power fluctuations in turbulence

Cited by in corpus (5)

• Coherent structures at the origin of time irreversibility in wall turbulence
• Non-equilibrium Ensembles for the three-dimensional Navier-Stokes Equations
• Viscosity, Reversibillity, Chaotic Hypothesis, Fluctuation Theorem and Lyapunov Pairing
• Equivalence of nonequilibrium ensembles: Two-dimensional turbulence with a dual cascade
• Poles, Shocks and Tygers: The Time-reversible Burgers equation